COLLEGE  OF  AGRICULTURE 
DAVIS,  CALIFORNIA 


- 


PRINCIPLES 

OF 


QUANTITATIVE  ANALYSIS 

AN  INTRODUCTORY  COURSE 


BY 

WALTER  C.  BLASDALE,  PH.  D. 

Associate  Professor  of  Chemistry  in  the  University  of  California 


70  ILLUSTRATIONS 


ERRATA 

Page  87,  6th  line  from  bottom,  for  180°  read  120°. 
Page  87,  6th  line  from  bottom,  for  250°  read  180°. 
Page  88,  17th  line  from  top,  after  512°  add  "  a  small  amount  of ; 


NEW  YOKK 

D.  VAN  NOSTRAND  COMPANY 

25  PARK  PLACE 
1914 

UNIVERSITY  OF  CALIFORNIA 

LIBRA,  vi 

COLLEGE  OF  A  .R1CULTURE 
DAVIS 


COPYRIGHT,  1914, 

BY 
D.  VAN   NOSTRAND   COMPANY 


Stanhope  ipress 

F.  H.  GILSON  COMPANY 
BOSTON.  U.S.A. 


PREFACE 


THE  introductory  course  in  quantitative  analysis  is  expected  to 
meet  a  variety  of  needs.  For  a  limited  number  of  students  it 
represents  the  beginning  of  a  course  of  training  which  ultimately 
leads  to  the  ability  to  do  effective  work  as  a  professional  analyst. 
For  others  it  represents  merely  one  of  the  necessary  features  of 
the  training,  which  every  student  who  aspires  to  the  title  of 
chemist  must  complete.  For  still  others  the  object  to  be  gained 
is  a  general  survey  of  the  methods  of  quantitative  analysis,  and 
the  ability  to  comprehend  and  make  intelligent  use  of  the  results 
obtained  by  it,  especially  as  applied  to  the  various  branches  of 
both  pure  and  applied  science. 

Some  of  the  other  difficulties  which  arise  in  presenting  the  sub- 
ject are,  the  limited  amount  of  time  which  can  be  devoted  to  it; 
the  large  amount  of  personal  supervision  and  assistance  which 
should  be  given  each  student,  if  he  is  to  acquire  the  necessary 
manipulative  skill  with  the  least  Expenditure  of  time  and  effort; 
and  the  inability  of  the  instructor  to  furnish  the  student  with  an 
adequate  supply  of  platinum  ware  and  of  many  of  the  conven- 
iences and  special  forms  of  apparatus,  with  which  it  is  desirable 
the  student  should  become  acquainted. 

In  this  book  the  attempt  has  been  made  to  meet  these 
difficulties  by  outlining  the  entire  field  covered  by  the  subject; 
that  is,  by  presenting  it  from  the  standpoint  of  a  comprehensive 
scheme  of  classification,  which  is  based  upon  the  different  types  of 
chemical  and  physical  equilibrium.  By  adopting  this  method 
of  presentation  it  becomes  readily  possible  to  discuss  the  theory 
of  all  classes  of  quantitative  processes  from  the  point  of  view  of 
modern  theoretical  chemistry,  which  forms  the  only  logical  basis 
for  effective  work  in  analytical  chemistry,  and  incidentally  to 


iv  ^REFACE 

add  to  the  student's  experience  in  dealing  with  the  factors  which 
affect  equilibrium. 

After  the  general  theory  underlying  each  type  of  process  has 
been  presented,  a  number  of  examples  designed  to  illustrate  it 
are  discussed  and  described  in  detail.  The  number  outlined  is 
larger  than  can  be  made  use  of  in  the  introductory  course  usually 
given,  but  can  be  reduced  to  a  single  illustration  from  each  class 
if  necessary.  Altho  especial  emphasis  has  been  placed  upon  its 
theoretical  features,  the  fact  that  the  subject  is  essentially  a 
practical  one,  and  that  the  student's  interest  is  most  easily  main- 
tained when  he  is  required  to  solve  practical  problems,  the  results 
of  which  cannot  be  foretold,  has  not  been  lost  sight  of.  Hence  a 
large  number  of  the  illustrations  chosen  are  practical  problems, 
which  have  been  selected  from  a  variety  of  fields  and  which  are 
solved  by  the  use  of  methods  employed  in  practical  work.  It  is 
assumed  that  as  far  as  possible,  individual  samples,  whose  compo- 
sition is  known  only  to  the  instructor,  will  be  given  out  for  these 
determinations. 

In  the  development  of  these  illustrations,  the  attempt  is  made 
to  make  use  of  as  great  a  variety  of  principles  and  methods  of 
procedure  as  possible,  and  to  develop  the  student's  ability  to 
make  use  of  them  by  assigning  for  solution  a  series  of  questions 
and  problems;  those  outlined  are  offered  as  suggestions  only,  and 
should  be  modified  from  year  to  year. 

It  is  scarcely  necessary  to  add  that  most  of  the  ideas  which  have 
been  made  use  of  are  not  new.  Especial  acknowledgment  should 
be  made  to  Ostwald,  whose  "Grundlagen  der  analytischen 
Chemie"  represents  the  first  attempt  to  summarize  those  features 
of  theoretical  chemistry  which  can  be  most  profitably  applied  to 
analytical  chemistry.  Acknowledgment  of  some  of  the  other 
sources  of  information  will  be  found  in  the  text,  but  the  limitation 
imposed  on  the  size  of  the  book  has  made  it  impossible  to  ac- 
knowledge all  of  them.  ^r  Q  B. 
BERKELEY,  CAL. 
July  I,  1914. 


TABLE  OF  CONTENTS 


PAGE 

PREFACE iii 

CHAPTER 

I.   INTRODUCTORY  STATEMENTS  AND  DEFINITIONS 1 

Section  One.  —  General  Features  of  Gravimetric  Processes 

II.   THE  METHOD  OF  WEIGHING 9 

I.  Theory  of  the  Use  of  the  Balance.  II.  Rules  for  the 
Use  of  the  Balance.  III.  Details  of  Procedure  for  Determina- 
tion of  Point  of  Rest.  IV.  Details  of  Procedure  for  Determina- 
tion of  Weight  of  a  Watch  Glass.  V.  Details  of  Procedure  for 
Calibration  of  a  Set  of  Weights.  VI.  Questions  and  Problems, 
Series  1. 

III.  PREPARATION  OF  THE  SUBSTANCE  FOR  ANALYSIS 26 

IV.  THE  NATURE  AND  PROPERTIES  OF  SOLUTIONS 30 

V.   THE  FACTORS  WHICH  DETERMINE  EQUILIBRIUM 41 

VI.   THE  CHEMICAL  ACTIVITY  OF  ELECTROLYTES 48 

VII.   METHODS  OF  PRODUCING  AND  APPLYING  HEAT 60 

VIII.   THE  REMOVAL  OF  UNDESIRABLE  CONSTITUENTS  BY  EVAPO- 
RATION         67 

IX.   THE  CALCULATION  OF  RESULTS 73 

Section  Two.  —  Gravimetric  Gas-evolution  Processes 

X.   GENERAL  FEATURES  OF  GAS-EVOLUTION  PROCESSES 78 

XI.   DETERMINATION  OF  WATER  IN  GYPSUM 87 

I.   Facts  upon  Which  the  Determination  Is  Based.     II. 
Details  of  the  Method  of  Procedure.     III.   Further  Details  Re- 
garding   the    Determination.      IV.     Questions    and    Problems, 
Series  2. 

v 


VI  TABLE  OF  CONTENTS 

CHAPTER  PAGE 

XII.   DETERMINATION  OF  WATER  IN  CRYSTALLIZED  COPPER  SUL- 

FATE 92 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Construction  of  the  Apparatus.  III.  Details  of  the  Method  of 
Procedure.  IV.  Questions  and  Problems,  Series  3. 

XIII.  DETERMINATION  OF  CARBON  DIOXIDE  IN  LIMESTONE 99 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Preparation  of  the  Apparatus.  III.  Details  of  Method  of  Pro- 
cedure. IV.  Questions  and  Problems,  Series  4. 

XIV.  DETERMINATION  OF  CARBON  DIOXIDE  IN  BAKING  POWDER.     103 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Construction  of  the  Apparatus.  III.  Outline  of  Method  of  Pro- 
cedure. IV.  Questions  and  Problems,  Series  5. 

XV.   DETERMINATION  OF  MERCURY  IN  AN  ORE 107 

I.  Facts  Upon  Which  the  Method  Is  Based.  II.  Outline 
of  Method  of  Procedure. 


Section  Three.  —  Gravimetric  Precipitation  Processes 

XVI.   GENERAL  THEORY  OF  PRECIPITATION  PROCESSES Ill 

XVII.   FILTERING,  WASHING  AND  IGNITING  PRECIPITATES 118 

XVIII.   THE  PHENOMENA  OF  OCCLUSION 129 

XIX.   GENERAL  THEORY  OF  ELECTROYLTIC  SEPARATIONS 137 

XX.   DETERMINATION  OF  CHLORINE  IN  SODIUM  CHLORIDE 150 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Outline  of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  6. 

XXI.   DETERMINATION  OF  MAGNESIUM  IN  MAGNESIUM  SULFATE..     155 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Outline  of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  7. 

XXII.  DETERMINATION  OF  IRON  IN  FERROUS  AMMONIUM  SULFATE.     159 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Details  of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  8. 


TABLE  OF  CONTENTS  vii 

CHAPTER  PAGE 

XXIII.  DETERMINATION  OF  SULFUR  IN  PYRITES 164 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Outline  of  Method  of  Procedure.  III.  Additional  Notes  on  the 
Determination.  IV.  Questions  and  Problems,  Series  9. 

XXIV.  SEPARATION  OF  CALCIUM  FROM  MAGNESIUM  AND  PARTIAL 

ANALYSIS  OF  LIMESTONE 171 

I.   Preliminary  Statements,  Facts  Upon  Which  the  Analysis 

Is  Based.    III.   Outline  of  Method  of  Procedure.    IV.   Questions 

and  Problems,  Series  10. 

XXV.  ANALYSIS  OF  ALLOYS  CONTAINING  TIN  AND  LEAD 180 

I.  Facts  Upon  Which  the  Analysis  Is  Based.  II.  Outline 
of  the  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  11. 

XXVI.  THE  ANALYSIS  OF  BRASS 185 

I.  Facts  Upon  Which  the  Analysis  Is  Based.  II.  Out- 
line of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  12. 

XXVII.  DETERMINATION  OF  SILICA  IN  A  HORNBLENDE 190 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Outline  of  Method  of  Procedure. 

Section  Four.  —  Greavimetric  Solution  and  Extraction  Processes 

XXVIII.   GENERAL  FEATURES  OF  SOLUTION  AND  EXTRACTION  PROC- 
ESSES      195 

XXIX.   DETERMINATION  OF  POTASSIUM  IN  CRUDE  POTASSIUM  SUL- 

FATE 205 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Outline  of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  13. 

XXX.   DETERMINATION  OF  CRUDE  FAT  IN  PEANUTS 210 

I.  Facts  Upon  Which  the  Method  Is  Based.  II.  Out- 
line of  Method  of  Procedure. 

XXXI.  ANALYSIS  OF  BLACK  POWDER 214 

I.  Facts  Upon  Which  the  Analysis  Is  Based.  II.  Out- 
line of  Method  of  Procedure. 


Vlll  TABLE  OF  CONTENTS 

Section  Five.  —  Partition  Processes 

CHAPTER  PAGE 

XXXII.   GENERAL  FEATURES  OF  PARTITION  PROCESSES 216 

XXXIII.  DETERMINATION  OF  NICKEL  IN  NICKEL  STEEL 221 

I.  Facts  Upon  Which  the  Determination  Is  Based.  II. 
Outline  of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  14. 

XXXIV.  DETERMINATION  OF  CAFFEINE  IN  TEA 226 

I.  Facts  Upon  Which  the  Determination  Is  Based.  2. 
Outline  of  Method  of  Procedure.  III.  Questions  and  Problems, 
Series  15. 

Section  Six.  —  General  Features  of  Volumetric  Processes 

XXXV.   THEORY  OF  VOLUMETRIC  PROCESSES 230 

XXXVI.   MEASUREMENT  OF  SOLUTIONS  USED 236 

I.  Sources  and  Methods  of  Avoiding  Errors.  II.  Details 
of  Method  for  Calibration  of  Volumetric  Apparatus.  III.  Ques- 
tions and  Problems,  Series  16. 

XXXVII.  SYSTEMS  USED  IN  THE  PREPARATION  OF  STANDARD  SOLU- 
TIONS       247 

Section  Seven.  —  Volumetric  Processes  Involving  Precipitation 

XXXVIII.   DETERMINATION  WHICH  DEPEND   UPON  THE  USE  OF  A 

STANDARD  SOLUTION  OF  SILVER  NITRATE 252 

I.  Theory  Upon  Which  the  Methods  Depend.  II.  Prep- 
aration and  Standardization  of  a  Orte-tenth  Normal  Solution  of 
Silver  Nitrate.  III.  Determination  of  Chlorine  in  Kainite.  IV. 
Determination  of  Chlorine  in  Tap  Water.  V.  Determination  of 
Potassium  Cyanide  in  Commercial  Cyanide.  VI.  Questions  and 
Problems,  Series  17. 

XXXIX.  DETERMINATION  OF  ZINC  BY  MEANS  OF  A  SOLUTION  OF 

POTASSIUM  FERROCYANIDE 263 

I.  Theory  Upon  Which  the  Method  Depends.  II.  Ap- 
plication of  the  Method  to  the  Analysis  of  Zinc  Ores.  III.  Out- 
line of  Method  for  the  Preparation  and  Standardization  of  the 
Ferrocyanide  Solution.  IV.  Outline  of  Method  for  Determination 
of  Zinc  in  an  Ore.  V.  Questions  and  Problems,  Series  18. 


TABLE  OF  CONTENTS  ix 

Section  Eight.  —  Volumetric  Processes  Involving  Neutralization 
CHAPTER  PAGE 

XL.  GENERAL  THEORY  OF  NEUTRALIZATION  PROCESS 273 

XLI.  APPLICATIONS  OF  THE  METHODS  OF  ACIDIMETRY  AND  ALKA- 
LIMETRY. . 286 

I.  Determination  of  Acids  and  Acid  Salts.  II.  Deter- 
mination of  Bases  and  Basic  Salts.  III.  Determination  of  Salts 
of  Weak  Acids  andj  Bases.  IV.  Indirect  Determinations.  V. 
Questions  and  Problems,  Series  19. 

XLII.   THE  PREPARATION  OF  STANDARD  SOLUTIONS  OF  ACIDS  AND 

BASES 293 

I.  Factors  to  be  Considered.  II.  Outline  of  Method  for 
Preparation  of  Semi-normal  Acid  and  Alkali.  III.  Experiments 
with  Indicators.  IV.  Questions  and  Problems,  Series  20. 

XLIII.   DETERMINATIONS  WITH  A  STANDARD  ACID  AND  BASE 299 

I.  Determination  of  the  Strength  of  Concentrated  Sul- 
furic  Acid.  II.  Determination  of  the  Acidity  of  Vinegar.  III. 
Determination  of  Potassium  Bitartrate  in  Argol.  IV.  Deter- 
mination of  Boric  Anhydride  in  a  Natural  Borate.  V.  The 
Analysis  of  Commercial  Alkalies.  VI.  Determination  of  Crude 
Protein  in  Flour.  VII.  Questions  and  Problems,  Series  21. 


Section  Nine.  —  Volumetric  Processes  Involving  Oxidation 
XLIV.   GENERAL  FEATURES  OF  PROCESSES  INVOLVING  OXIDATION     306 

XLV.  DETERMINATIONS  WITH  POTASSIUM  PERMANGANATE 314 

I.  Potassium  Permanganate  as  an  Oxidizing  Agent.  II. 
Preparation  and  Standardization  of  a  Permanganate  Solution. 
III.  Determination  of  Iron  in  Cast  Iron.  IV.  Determination  of 
Potassium  Nitrite  in  the  Commercial  Salt.  V.  Determination  of 
Calcium  in  Limestone.  VI.  Questions  and  Problems,  Series  22. 

XLVI.  DETERMINATIONS  WITH  POTASSIUM  DICHROMATE 328 

I.  Potassium  Dichromate  as  an  Oxidizing  Agent.  II. 
Preparation  and  Standardization  of  a  Dichromate  Solution.  III. 
Determination  of  Iron  in  an  Ore.  VI.  Determination  of  Chrom- 
ium in  Chromite.  V.  Questions  and  Problems,  Series  23. 


X  TABLE  OF  CONTENTS 

CHAPTER  %     PAGE 

XLVII.   DETERMINATIONS  WITH    IODINE   AND   SODIUM    THIOSUL- 

»  FATE 339 

I.  General  Features  of  lodometric  Processes.  II.  Clas- 
sification of  lodometric  Processes.  III.  Outline  of  Method  for 
Preparation  of  Solutions.  IV.  Determination  of  Arsenic  in  Paris 
Green.  V.  Determination  of  Copper  in  Brass.  VI.  Determina- 
tion of  Copper  in  a  Cholcopyrite  Ore.  VII.  Questions  and  Prob- 
lems, Series  24. 

Section  Ten.  —  Physico-chemical  Processes 
XLVIII.   THEORY  OF  PHYSICO-CHEMICAL  METHODS 350 

XLIX.   PROCESSES   BASED   UPON  THE    DETERMINATION   OF  THE 
SPECIFIC  GRAVITY  OR  SPECIFIC  VOLUME  OF  SOLIDS  OR 

LIQUIDS 357 

I.  General  Features  of  the  Method.  II.  Analysis  of  a 
Lead-tin  Alloy.  III.  Determination  of  Sulfuric  Acid  in  a  Com- 
mercial Sample.  IV.  Determination  of  the  Specie  Gravity  of 
Crude  Petroleum.  V.  Questions  and  Problems,  Series  25. 

L.    COLORIMETRIC   PROCESSES 370 

I.  General  Features  of  Colorimetric  Processes.  II.  De- 
termination of  Manganese  in  Cast  Iron  or  Steel.  III.  Deter- 
mination of  Copper  in  a  Copper  Slag. 

APPENDICES 381 

I.  Table  of  Logarithms.    II.  Table  of  Specific  Gravities  of  Sulfuric 
Acid.    III.  List  of  Apparatus  Needed. 


QUANTITATIVE  CHEMICAL  ANALYSIS 

CHAPTER  I 

INTRODUCTORY   STATEMENTS  AND   DEFINITIONS 

Importance  of  Quantitative  Analysis.  Quantitative  analysis 
has  for  its  object  the  determination  of  the  quantity  of  some  element 
or  compound  present  in  a  particular  substance.  The  result  of 
the  determination  is  usually  expressed  as  a  percentage,  ordinarily 
by  weight,  but  sometimes  by  volume,  of  the  substance  concerned. 

The  subject  is  of  importance  from  a  number  of  standpoints. 
An  accurate  evaluation  of  most  of  the  important  objects  of  com- 
merce, and  determination  of  their  fitness  for  certain  purposes, 
cannot  be  made  until  their  quantitative  composition  has  been 
determined.  In  many  manufacturing  industries  the  raw  products 
used  are  purchased,  and  the  finished  products  obtained  are  sold, 
on  the  basis  of  the  results  shown  by  their  analysis;  further,  the 
entire  process  of  manufacture  is  often  controlled  by  means  of 
analyses  of  the  various  products,  for  such  analyses  enable  the 
manufacturer  to  determine  whether  each  of  the  various  stages  of 
the  process  have  been  properly  carried  out,  and  to  reduce  wastes 
and  losses  to  a  minimum. 

In  the  study  of  many  branches  of  natural  science  the  investiga- 
tor is  often  obliged  to  depend  upon  quantitative  analyses  for  the 
identification  and  comparison  of  the  substances  with  which  he  is 
concerned,  and  is  frequently  enabled  to  trace  the  laws  which  govern 
the  changes  taking  place  in  these  substances  through  the  study  of 
the  results  of  their  analysis.  The  present  science  of  chemistry 

1 


2  QUANTITATIVE  CHEMICAL  ANALYSIS 

is  based  very  largely  upon  the  employment  of  quantitative  methods 
in  the  study  of  chemical  changes;  the  sciences  of  ^geology  and 
physiology  have  been  very  largely  developed  by  the  use  of  data 
gathered  through  the  employment  of  quantitative  methods. 

The  subject  has  also  a  certain  educational  value,  in  that  it 
concentrates  the  attention  of  the  student  upon  a  limited  number 
of  chemical  transformations;  teaches  him  to  observe  critically  all 
of  the  changes  which  take  place  in  the  material  with  which  he  is 
dealing,  and  to  devise  methods  of  avoiding '  certain  undesirable 
effects  and  take  advantage  of  others  which  are  desirable. 
>  Range  of  the  Subject.  It  is  evident  from  the  preceding  para- 
graphs that  the  field  of  quantitative  analysis  extends  over  an 
extremely  wide  range  of  subjects,  for  the  analyst  may  be  called 
upon  to  determine  the  quantitative  composition  of  any  material 
object  whatever.  The  analysis  of  substances  containing  a  number 
of  constituents  often  presents  a  problem  of  much  complexity,  and 
much  ingenuity  has  been  used  in  devising  methods,  which  can  be 
employed  to  determine  those  elements  and  compounds,  that  are 
of  importance  from  either  a  practical  or  scientific  standpoint,  with 
the  requisite  accuracy  and  with  the  minimum  expenditure  of  time 
and  effort.  The  acquirement  of  a  working  knowledge  of  even  the 
more  important  of  these  methods  is  a  task  of  considerable  mag- 
nitude, and  the  subject  forms  one  of  the  most  comprehensive 
branches  of  the  science  of  chemistry. 

Types  of  Quantitative  Processes.  A  sufficiently  comprehen- 
sive and  entirely  satisfactory  classification  of  all  the  methods 
included  under  the  general  head  of  quantitative  analysis  is  not 
easily  formulated.  All  of  the  more  important  methods  in  general 
use  may  be  grouped  under  four  classes,  which  differ  so  fundamen- 
tally in  method  of  procedure  that  it  is  desirable  to  discuss  them 
separately. 

Gravimetric  methods  are  those  in  which  the  determination  is 
effected  by  the  actual  separation  of  the  desired  constituent,  or 
some  product  which  bears  a  definite  quantitative  relation  to  it, 


INTRODUCTORY  STATEMENTS  AND   DEFINITIONS  3 

and  the  determination  of  the  weight  of  the  product  thus  separated. 
Thus  the  silver  can  be  determined  in  an  alloy  by  dissolving  a 
definite  weight  of  the  alloy  in  nitric  acid,  separating  the  silver 
present  as  insoluble  silver  chloride,  weighing  the  latter,  and  calcu- 
lating the  weight  of  silver  present  from  the  factor  representing  the 
ratio  of  the  atomic  weight  of  silver  to  the  molecular  weight  of  silver 
chloride. 

The  distinguishing  feature  of  all  gravimetric  processes  is  the 
mechanical  separation  of  a  product,  the  weight  of  which  bears  a 
known  relation  to  the  weight  of  the  substance  which  is  being 
determined,  from  the  substance  being  analyzed.  Such  separations 
are  possible  only  when  there  are  definite  surfaces,  which  represent 
the  limits  of  the  spaces  occupied  by  the  separated  substance  on  the 
one  hand,  and  the  original  mixture  on  the  other.  Expressed  in  the 
language  of  modern  theoretical  chemistry  every  gravimetric 
process  involves  a  series  of  chemical  and  physical  operations, 
which  bring  about  such  changes  in  the  original  substance  that  a 
new  " phase"  separates,  the  term  phase  being  used  to  designate  a 
mass  of  matter  which  is  physically  and  chemically  homogeneous. 
In  the  illustration  cited  the  separated  phase  took  the  form  of  a 
solid;  it  might  have  taken  the  form  of  a  gas,  or  of  a  second  liquid, 
which  does  not  mix  with  the  first,  and  a  logical  and  convenient 
basis  for  the  classification  of  gravimetric  processes  is  found  in  the 
type  of  "phase-transformation"  which  they  represent.  Such  a 
scheme  has  been  adopted  in  this  book,  and  separate  sections  are 
devoted  to  "gas  evolution  processes,"  in  which  a  new  gas  phase  is 
made  to  separate  from  a  solid  or  liquid;  "precipitation  processes," 
in  which  a  new  solid  phase  is  made  to  separate  from  a  liquid; 
"solution  and  extraction  processes,"  in  which  a  new  liquid  phase 
is  made  to  separate  from  a  solid;  and  "partition  processes,"  in 
which  a  new  liquid  phase  is  made  to  separate  from  a  liquid  phase. 
Volumetric  methods  are  those  in  which  the  amount  of  substance 
to  be  determined  is  estimated  by  measuring  the  volume  of  some 
reagent  of  known  concentration,  which  must  be  used  to  completely 


4  QUANTITATIVE   CHEMICAL  ANALYSIS 

transform  the  constituent  being  determined  into  some  other  form. 
The  actual  separation  of  a  particular  product  is  thereby  avoided. 
Thus  the  silver  can  also  be  determined  in  the  alloy  by  measuring 
the  amount  of  sodium  chloride  solution  of  known  strength  which 
must  be  added  to  a  solution  containing  a  known  weight  of  the 
alloy  to  precipitate  all  of  the  silver  as  chloride.  Volumetric 
processes  are  conveniently  classified  with  respect  to  the  type  of 
reaction  upon  which -they  are  based;  the  three  important  classes 
are  made  the  subject  of  separate  sections  of  this  book. 

Physico-chemical  methods  are  those  in  which  the  unknown 
substance  is  determined  by  measuring  some  one  of  the  various 
physical  properties  of  a  solution  containing  a  known  concentration 
of  the  sample  under  investigation,  and  comparing  with  the  corre- 
sponding properties  of  solutions  containing  known  concentrations 
of  the  substance  to  be  determined.  They  are  of  rather  restricted 
application,  and  are  not  strictly  speaking  chemical  processes,  but 
they  are  so  frequently  used  by  the  analytical  chemist  that  it  is 
customary  to  group  them  with  these. 

Gas-analysis  methods  which  are  based  upon  the  direct  measure- 
ment of  gas  volumes  form  still  a  fourth  group.  They  are  used  not 
only  for  the  analysis  of  gaseous  mixtures  but  also  for  the  deter- 
mination of  a  large  number  of  substances  which  yield  gaseous 
products  when  submitted  to  the  action  of  certain  reagents.  The 
successful  use  of  these  methods  demands  the  employment  of  a 
large  amount  of  specialized  forms  of  apparatus;  it  has  not  been 
thought  desirable  to  consider  them  in  this  book. 

The  Training  and  Skill  Required.  Success  in  quantitative 
work  demands  first  of  all  a  certain  amount  of  dexterity  in  perform- 
ing the  mechanical  operations  involved.  Training  of  the  hand  and 
eye,  which  results  in  the  formation  of  habits  of  deftness  and 
precision  in  manipulation  is  an  essential  prerequisite  to  work  in 
this  field.  Certain  individuals  are  able  to  acquire  this  skill  with 
comparative  ease,  but,  unfortunately,  by  far  the  great  majority  of 
persons  can  acquire  it  only  through  patient  and  persistent  appli- 


INTRODUCTORY  STATEMENTS  AND   DEFINITIONS  5 

cation.  The  beginner  cannot  be  expected  to  do  as  rapid  or  as 
accurate  work  as  the  trained  analyst,  and  only  actual  experience 
with  a  great  variety  of  quantitative  processes  will  teach  the  most 
effective  methods  of  dealing  with  the  problems  which  constantly 
arise  in  the  execution  of  quantitative  work  and  enable  him  to 
reduce  to  a  minimum  those  errors  of  the  process  which  depend 
upon  manipulative  skill. 

Absolute  Honesty  Demanded.  Of, the  many  qualifications 
which  the  successful  analyst  must  possess  none  equals  in  impor- 
tance that  of  unimpeachable  honesty.  It  is  unnecessary  to  con- 
demn or  to  point  out  the  ultimate  effect  of  the  intentional  falsifi- 
cation of  the  results  obtained  in  any  line  of  scientific  work  to  any 
intelligent  student;  but  even  when  there  is  no  desire  to  misrepre- 
sent, care  must  be  taken  to  overcome  any  temptation  which  may 
arise  to  pick  and  choose  results  on  the  basis  of  some  preconceived 
notion  of  their  comparative  accuracy.  If,  for  example,  a  number 
of  results  have  been  obtained  with  the  same  process,  the  fact  that 
some  one  of  these  agrees  most  nearly  with  what  is  supposed  to  be 
the  correct  result  does  not  justify  suppressing  the  others,  unless 
there  is  positive  evidence  of  the  fact  that  they  involve  errors  which 
do  not  appear  in  the  one  which  it  is  proposed  to  accept.  If  the 
student  finds  himself  unable  to  do  as  good  work  as  a  more  experi- 
enced or  more  fortunately  endowed  neighbor  he  should  not  hesitate 
to  frankly  acknowledge  the  fact,  and  should  devote  his  efforts  to 
increasing  his  proficiency  rather  than  to  concealing  his  lack  of  it. 
Deficiencies  of  this  kind  can  be  overcome  through  intelligent  and 
well-directed  effort,  and  the  satisfaction  which  results  from  over- 
coming them  is  well  worth  the  effort  which  it  may  cost.  The 
ability  to  do  good  analytical  work  represents  a  non-transferable 
asset  of  no  small  commercial  value. 

Theoretical  Knowledge  Necessary.  Although  any  person  who 
has  acquired  the  necessary  manipulative  skill  may  be  able  to 
execute  the  details  of  a  carefully  described  quantitative  process, 
his  ability  to  make  effective  use  of  the  process  will  be  decidedly 


6  QUANTITATIVE  CHEMICAL  ANALYSIS 

limited,  owing  to  the  fact  that  unforeseen  contingencies,  which 
his  carefully  worded  description  did  not  allow  for,  constantly  arise. 
It  is  only  through  a  definite  knowledge  of  the  theory  of  each  step 
of  the  process  that  the  analyst  can  work  intelligently  and  effec- 
tively; the  mechanical  performance  of  such  operations  without 
understanding  the  reason  for  each  step  is  not  worthy  of  being 
dignified  by  the  term  "  quantitative  analysis." 

It  should  also  be  noted  that  the  method  employed  must  be 
adapted  to  the  purpose  for  which  the  desired  result  is  to  be  used. 
Frequently  the  rapidity  with  which  a  result  can  be  obtained  is  of 
greater  importance  than  extreme  accuracy,  and  in  such  cases  time 
and  labor  can  be  saved  by  neglecting  certain  of  the  details  com- 
monly used  or  by  employing  certain  " short-cut"  methods.  Every 
quantitative  determination  is,  therefore,  a  specific  problem  in 
itself,  and  an  analysis  of  the  various  factors  concerned  in  every 
detail  of  the  proposed  method  may  render  it  possible  to  increase 
either  the  accuracy  of  the  work,  or  the  productive  capacity  of  the 
analyst.  An  accurate  sense  of  proportion  and  judgment,  as  to  the 
importance  and  necessity  of  the  details  of  quantitative  work  must 
be  developed  if  the  greatest  efficiency  is  to  be  attained. 
:  The  Literature  of  the  Subject.  A  vast  amount  of  experi- 
mental work  having  for  its  object  the  development  of  new,  or 
perfection  of  old,  methods  of  analysis  is  being  carried  out  con- 
tinually. *  The  results  are  published  either  in  certain  special 
journals  devoted  to  this  branch  of  chemistry,  such  as  the  Zeit- 
schrift  fur  analytische  Chemie  (Wiesbaden)  and  the  Analyst 
(London)  or  in  the  more  numerous  chemical  periodicals  of  a  more 
general  character.  Especial  importance  should  be  attached  to 
the  reports  of  Committees  and  Associations,  who  cooperate  in 
making  tests  of  analytical  methods  under  as  nearly  identical 
conditions  as  possible.  Such,  for  instance,  is  the  work  of  the 
Official  Association  of  Agricultural  Chemists  or  of  the  various 
Committees  of  the  American  Chemical  Society.  The  progressive 
analyst  will  find  it  necessary  to  keep  in  touch  with  the  newer 


INTRODUCTORY  STATEMENTS  AND  DEFINITIONS          7 

developments  of  the  subject,  and  even  the  beginner  will  derive 
much  profit  and  inspiration  from  consulting  the  original  sources 
of  information  upon  which  the  methods  he  uses  are  based;  hence, 
references  to  a  limited  number  of  important  articles  are  added  to 
some  of  the  processes  described  in  this  book.  Although  a  number 
of  works  which  attempt  to  summarize  all  of  the  more  important 
quantitative  methods  are  available,  more  comprehensive  and 
usually  more  up-to-date  information  can  be  found  in  the  numerous 
manuals  devoted  to  the  elaboration  of  the  methods  which  are 
especially  adapted  to  the  analysis  of  particular  classes  of  materials, 
such  as  ores  and  metallurgical  products,  alloys,  rocks,  soils  and 
fertilizers,  foods,  etc. 

Proposed  Plan  of  Work.  The  object  of  this  book  is  to  present 
the  fundamental  principles  used  in  the  general  subject  of  quanti- 
tative analysis,  and  outline  a  method  by  which  a  working  knowl- 
edge of  the  subject  can  be  attained.  In  the  plan  of  work  here 
adopted  the  theory  of  each  of  the  larger  groups  of  quantitative 
processes  is  first  discussed,  then  a  limited  number  of  typical 
illustrations  are  described  in  detail  and  the  various  sources  of 
error  and  further  applications  of  the  method  suggested.  A  series 
of  questions  and  problems  designed  to  point  out  the  reasons  for 
certain  features  of  the  methods  and  emphasize  the  general  prin- 
ciples used  are  appended  to  most  of  these  descriptions.  In  the 
elaboration  of  each  of  the  different  classes  of  processes  much  matter 
of  a  more  general  character  finds  constant  use;  this  has  been 
presented  in  brief  form  in  the  series  of  chapters  forming  the  first 
section  of  the  book.  Familiarity  with  all  of  the  facts  there  pre- 
sented is  not  an  essential  prerequisite  to  actual  work  with  the 
methods  described  in  the  subsequent  sections;  all  of  it  is  necessary 
to  a  comprehensive  knowledge  of  the  principles  of  quantitative 
analysis,  and  these  chapters  should  be  carefully  read  and  digested 
as  progress  is  made  in  the  practical  part  of  the  work. 

Strength  of  Reagents  Used.  A  large  number  of  the  reagents 
used  in  quantitative  analysis  are  prepared  for  one  specific  purpose 


8  QUANTITATIVE  CHEMICAL   ANALYSIS 

only;  the  method  of  preparing  such  reagents  will  be  given  in  the 
descriptions  of  the  processes  in  which  they  are  used.  The  strength 
of  certain  reagents  which  are  used  in  a  great  variety  of  processes 
are  given  below. 

Dilute  ammonium  hydroxide,  made  by  adding  two  and  one-half 
volumes  of  water  to  one  of  concentrated  ammonium  hydroxide 
(sp.  gr.  0.9).  One  cc.  of  the  diluted  reagent  contains  0.102  gm. 
NH3.  It  is  6-normal. 

Dilute  acetic  acid,  made  by  adding  three  volumes  of  water  to 
one  of  80  per  cent  acid.  One  cc.  contains  0.2  gm.  C2H402. 

Concentrated  hydrochloric  acid.     One  cc.  contains  0.44  gm. 
HC1.     Its  specific  gravity  is  1.19.     It  is  12-normal. 
1    Dilute  hydrochloric  acid,  made  by  adding  one  volume  of  water 
to  one  of  the  concentrated  acid.     One  cc.  contains  0.22  gm.  HC1. 
Its  specific  gravity  is  1.10.     It  is  6-normal. 

Concentrated  nitric  acid.  One  cc.  contains  0.99  gm.  HNOs. 
Its  specific  gravity  is  1.42.  It  is  15-normal. 

Dilute  nitric  acid,  made  by  adding  one  and  six-tenths  volumes  of 
water  to  one  of  concentrated  acid.  One  cc.  contains  0.38  gm. 
HNOs.  Its  specific  gravity  is  1.2.  It  is  6-normal. 

Concentrated  sulfuric  acid.  One  cc.  contains  1.77  gm.  Its 
specific  gravity  is  1.84.  It  is  36-normal. 

Dilute  sulfuric  acid.  Made  by  adding  five  volumes  of  water 
to  one  of  the  concentrated  acid.  One  cc.  =  0.30  gm.  H2S04.  Its 
specific  gravity  is  1.19.  .It  is  6-normal. 


SECTION   I 
GENERAL  FEATURES   OF  GRAVIMETRIC   PROCESSES 


CHAPTER  II 

THE   METHOD   OF  WEIGHING 

I.   THEORY  OF  THE  USE  OF  THE  BALANCE 

Construction.  Quantitative  processes  involve  determinations 
of  the  relations  existing  between  two  masses  of  matter,  but  since 
both  masses  are  determined  by  means  of  a  beam  balance  under 
identical  conditions  the  distinction  between  mass  and  weight  can 
be  disregarded.  The  accuracy  of  such  processes  must  depend 
in  part  upon  the  accuracy  with  which  the  two  weighings  are  made, 
and  instrument  makers  have  developed  certain  forms  of  balances 
known  as  " analytical  balances"  the  use  of  which  makes  it  possible 
to  reduce  the  errors  from  this  source  to  insignificant  proportions. 
The  details  of  the  mechanism  used  by  different  makers  for  the 
adjustment  and  protection  of  such  balances  vary,  but  since  all  are 
based  upon  the  use  of  essentially  the  same  principles,  only  one 
type  will  be  described  here. 

The  beam  of  such  a  balance  is  represented  in  Fig.  1.  It  is  con- 
structed of  such  material,  and  in  such  a  form,  as  to  combine  the 
maximum  degree  of  rigidity  and  strength,  with  the  minimum 
weight.  It  is  suspended  at  its  center  on  a  horizontal  axis,  which 
is  made  of  agate  and  accurately  ground  to  a  knife-blade  edge,  as 
shown  at  A  of  the  figure.  This  axis  rests  upon  a  strip  of  polished 
agate  supported  upon  the  top  of  a  pillar,  and  the  beam  is  free  to 
turn  in  a  vertical  plane  about  this  axis.  Two  other  knife-blade 


10 


QUANTITATIVE  CHEMICAL  ANALYSIS 


edges  B  and  Bf,  which  are  of  a  similar  construction,  but  with  edges 
turned  upwards  instead  of  downwards,  are  fixed  at  the  two  ends 
and  equidistant  from  the  center.  These  edges  sustain  specially 
constructed  stirrups,  which  are  also  provided  with  strips  of  agate, 


15 


Fig.  1.  —  Beam  of  an  Analytical  Balance 

C  and  C'  of  the  figure,  at  the  points  of  contact;  from  them  are 
suspended  two  pans,  one  of  which  supports  the  substance  being 
weighed,  and  the  other  the  weights  used.  The  beam  may  be 
regarded  as  a  compound  lever  in  which  the  fulcrum  is  at  the  axis 
of  suspension.  If  the  two  arms  are  of  equal  length,  and  if  the 
pans  and  the  loads  which  they  contain  are  of  equal  weight,  the 
effect  of  the  force  of  gravity  upon  the  two  ends  of  the  beam  is 

identical,  and  a  depression  of  one  end  of 
the  beam  will  produce  a  series  of  vibra- 
tions similar  to  those  of  a  pendulum. 

The  process  of  weighing  consists  in  plac- 
ing the  substance  whose  weight  is  to  be 
Fig.  2.  —  Scale  of  Balance     ,   ,         .       ,.  °  .   , 

determined  in  one  pan,  and  adding  weights 

to  the  other  until  the  two  counterbalance  each  other.  This  point  can 
be  recognized  by  observing  the  movements  of  the  beam,  and  a 
pointer,  the  upper  part  of  which  is  shown  at  D,  is  attached  to  it 
for  the  purpose  of  magnifying  these  movements;  a  small  ivory 
scale,  represented  by  Fig.  2,  is  placed  just  back  of  the  end  of  the 
pointer,  in  order  to  make  it  possible  to  measure  and  record  the 
magnitude  of  these  movements  with  respect  to  the  central  axis. 


THE  METHOD  OF  WEIGHING  11 

The  center  of  this  scale,  which  is  directly  below  the  axis  of  sus- 
pension, should  be  marked  10,  the  tenth  division  to  the  left  zero, 
and  the  tenth  to  the  right  twenty;  this  method  of  marking  the 
scale  at  once  indicates  whether  the  numbers  recorded  are  to  the 
left  or  the  right  of  the  center. 

As  the  movement  of  the  beam  is  greatly  retarded  by  friction, 
and  as  the  friction  losses  increase  very  rapidly  as  the  knife-blade 
edges  lose  their  sharpness,  it  is  necessary  to  protect  these  bearings 
against  needless  wear;  hence,  analytical  balances  are  often  pro- 
vided with  two  sets  of  rests,  known  as  "beam  rests"  and  "pan 
rests"  respectively.  The  beam  rests  are  controlled  by  a  milled 
button,  placed  at  the  center  and  on  a  level  with  the  floor  of  the 
balance  case.  When  rotated  it  turns  an  eccentric,  which  raises  a 
rod  passing  through  the  center  of  the  pillar  of  the  balance,  and  this 
in  turn  raises  two  hinged  arms  E  and  Er,  which  lift  the  knife- 
blade  edge  A  from  the  agate  plate,  and  also  the  stirrups  sustaining 
the  pans  from  the  knife-blade  edges 
B  and  E'  on  which  they  rest.  The 
hinged  arms  are  also  provided  with 
two  studs  F  and  F',  which  fit  into  a 
cup  and  a  trough  terminating  the  two 
studs  G  and  G',  fastened  to  the  beam. 
The  effect  of  raising  and  lowering  the 
beam  rests  is  to  bring  the  beam  into 
exactly  the  same  position  with  re-  .=Ua 
spect  to  the  agate  plate  upon  which  Fig.  3.  _  Base  of  Balance  Case 
it  rests. 

The  pan  rests  are  controlled  by  a  small  knob  placed  at  the  left 
of  the  center,  as  shown  at  /  of  Fig.  3.  When  a  slight  pressure  is 
applied  to  this  button,  the  rod  to  which  it  is  attached  moves  the 
lever  J  which  carries  two  arms  K  and  Kf  and  cause  these  to  drop. 
Ordinarily  these  arms  impinge  upon  the  bottom  of  the  pans  L  and 
L'  and  prevent  needless  vibration  and  wear  of  the  bearings  B  and 
B',  but  when  they  drop  the  beam  is  free  to  vibrate.  As  a  protection 


12  QUANTITATIVE  CHEMICAL  ANALYSIS 

against  dust,  moisture  and  air  currents,  the  entire  apparatus  is 
enclosed  in  a  glass  case,  one  side  of  which  consists  of  a  movable 
slide  of  the  same  material. 

Conditions  which  Determine  Accuracy.  An  accurate  com- 
parison of  the  relative  magnitudes  of  two  masses  cannot  be  made 
with  such  a  balance  unless  certain  essential  conditions  are  complied 
with. 

First,  the  point  of  suspension  of  the  beam  should  be  equidistant 
from  the  points  of  suspension  of  the  two  pans,  for  if  these  distances 
differ  the  loads  sustained  by  the  two  arms  act  with  unequal  lever- 
ages. If  the  total  length  of  the  beam  is  known  the  difference  in 
the  lengths  of  the  two  arms  can  be  calculated  from  the  weights 
found  to  be  necessary  to  counterbalance  the  same  object,  when 
placed  first  on  one  pan  and  then  on  the  other.  If  we  represent  the 
length  of  the  right  arm  by  r,  that  of  the  left  arm  by  I,  the  true 
weight  of  the  object  by  W,  the  apparent  weight  when  placed  in  the 
left  pan  by  A,  and  when  placed  in  the  right  pan  by  A  +  a,  we  have, 
Ar  =  Wl,  also  W r  =  (A  +  a)  I 

If  we  multiply  these  two  equations  together  and  simplify  the 
resulting  expression  we  can  obtain  the  relation 

(r)2  :  (Q2  :  :  A  +  a  :  A. 

It  is  also  easy  to  show  that  the  true  weight  of  the  object  corre- 
sponds to  the  square  root  of  the  product  of  the  two  apparent 
weights,  or  since  the  two  differ  but  slightly,  it  is  represented  with 
sufficient  accuracy  by  the  average  of  the  apparent  weights.  Since 
it  is  not  possible  to  make  a  balance  whose  two  arms  are  absolutely 
equal,  this  method  of  " double  weighing'7  is  always  used  where 
extreme  accuracy  is  demanded.  The  error  which  might  result 
from  this  defect  in  the  construction  of  the  balance  can  usually  be 
neglected  if  the  same  pan,  usually  the  left-hand  one,  is  used  for  all 
the  weighings  concerned  in  every  determination  made. 

Second,  the  center  of  gravity  of  the  entire  system,  that  is,  of  the 
beam  and  the  two  loads  which  it  sustains,  must  be  slightly  below 


THE   METHOD  OF  WEIGHING  13 

the  point  of  suspension  of  the  beam.  If  the  reverse  relation  holds, 
the  system  is  in  unstable  equilibrium;  if  the  two  points  fall  to- 
gether, the  system  is  in  neutral  equilibrium,  and  vibration  of  the 
beam  even  with  equal  weights  is  impossible.  If  the  center  of 
gravity  of  the  system  is  too  far  below  the  point  of  suspension,  the 
deflection  produced  by  a  slight  excess  of  weight  in  either  pan  is  but 
slight,  and  the  balance  is  not  sufficiently  sensitive.  By  means  of 
a  small  weight,  which  slides  up  and  down  the  pointer,  but  which 
can  be  fixed  by  means  of  a  set  screw,  see  H  of  Fig.  1,  the  center  of 
gravity  can  be  lowered  or  raised.  If,  however,  this  distance  is 
made  too  small  the  retarding  effect  of  friction  is  relatively  greater, 
and  the  movements  of  the  beam  are  slow  and  uncertain. 

Third,  the  point  of  suspension  of  the  beam  and  of  the  two  pans 
must  be  very  nearly  on  the  same  horizontal  line;  otherwise, 
changes  in  the  loads  carried  by  the  pans  change  the  position  of  the 
center  of  gravity,  and  hence  the  sensitiveness.  Since  all  balance 
beams  yield  slightly  to  heavy  loads  it  is  impossible  to  comply  with 
this  condition  in  all  cases.  Manufacturers  usually  endeavor  to 
make  A  stand  as  much  below  the  line  joining  B  and  B',  when  the 
balance  is  empty  as  it  stands  above  this  line  when  the  pans  sustain 
the  maximum  permissible  load;  the  balance  should  then  show  the 
minimum  change  in  sensitiveness  with  an  average  load. 

Sensitiveness.  The  sensitiveness  of  a  balance  is  measured  by 
the  magnitude  of  the  angle,  corresponding  to  the  change  in  the 
position  of  the  pointer,  produced  by  a  slight  excess  of  weight  in 
either  pan.  Evidently  this  angle  must  increase  as  the  length  of 
the  beam  is  increased,  but  it  is  undesirable  to  increase  the  length 
of  the  beam  beyond  a  certain  maximum,  as  the  movements  of  the 
pointer  then  become  correspondingly  slow  (and  in  this  respect  the 
behavior  of  the  beam  differs  from  that  of  a  pendulum),  and 
the  time  occupied  in  making  a  weighing  is  materially  increased. 
The  sensitiveness  decreases  as  the  weight  of  the  beam  and  the  other 
factors  which  produce  friction  increase.  The  third,  and  perhaps 
most  important,  factor  is  the  adjustment  of  the  center  of  gravity 


14  QUANTITATIVE   CHEMICAL  ANALYSIS 

with  respect  to  the  point  of  suspension.  The  quantitative  ex- 
pression which  represents  the  relation  between  these  factors  is 
given  by  the  equation: 

LXW 


in  which  L  is  the  length  of  the  arm,  W  the  excess  of  weight  in  the 
pan,  D  the  distance  referred  to  above,  and  Q  the  weight  of  the 
beam. 

As  ordinarily  used  the  term  sensitiveness  represents  the  number 
of  scale  divisions  thru  which  the  pointer  is  deflected  by  one  milli- 
gram. Altho  it  is  desirable  to  make  the  sensitiveness  large  by 
reducing  the  value  of  Z),  it  cannot  be  reduced  below  a  certain 
limit,  which  depends  largely  upon  the  skill  used  in  the  construction 
of  the  balance  and  the  weight  of  the  beam,  or  the  movements  of 
the  pointer  become  so  variable  and  uncertain  that  the  point  of 
rest  cannot  be  determined  with  certainty.  It  should  be  possible 
to  so  adjust  the  balance  that  it  has  a  sensitiveness  of  from  1.5  to 
2  divisions. 

The  Point  of  Rest.  If  we  have  an  ideal  balance,  that  is,  one 
which  has  been  perfectly  constructed,  which  is  free  from  friction, 
and  which  is  loaded  with  equivalent  weights,  a  slight  depression 
of  one  end  of  the  beam  will  cause  the  beam  to  vibrate  back  and 
forth  and  the  pointer  to  move  an  equal  number  of  divisions  to  the 
right  and  to  the  left  of  the  central  point  of  the  ivory  scale  for  an 
indefinite  length  of  time.  Owing  to  friction,  and  various  faults 
of  construction,  there  is  a  constant  decrease  in  the  amplitude  of 
these  vibrations,  and  the  beam  finally  comes  to  rest.  This  posi- 
tion, as  indicated  by  the  position  of  the  pointer  with  reference  to 
the  divisions  of  the  ivory  scale,  is  called  the  "  point  of  rest7'  of  the 
balance,  and  is  constant  for  any  given  set  of  conditions.  Owing 
to  slight  variations  in  these  conditions,  accumulation  of  dust  on 
the  pans,  temperature  changes,  etc.,  this  point  may  vary  slightly 
from  day  to  day,  and  rarely  corresponds  exactly  with  the  center 
of  the  ivory  scale.  If  it  differs  from  it  greatly  the  balance  should 


THE  METHOD  OF  WEIGHING 


15 


be  readjusted  by  movement  of  one  of  the  two  buttons,  0  and  Of 
of  Fig.  1,  at  the  end  of  the  beam,  toward  or  away  from  the  point 
of  suspension  as  the  case  may  require. 

The  exact  position  of  the  point  of  rest  C  is  most  rapidly  and 
accurately  determined  by  noting  the  limits  of  a  series  of  vibrations, 
and  averaging  the  results.  If 
there  were  no  decrease  in  the 
amplitude  of  these  vibrations, 
one-half  the  sum  of  the  aver- 
ages of  the  positions  reached 
by  the  pointer  on  the  right  and 
left  respectively  would  give  the 
correct  position  of  the  point. 
Owing  to  this  decrement,  how- 
ever, this  is  strictly  true  only  when  an  even  number  of  readings  is 
made  on  one  side  and  an  odd  number  on  the  other,  as  considera- 
tion of  the  accompanying  diagram,  Fig.  4,  will  show.  In  this  dia- 
gram the  successive  positions  reached' are  designated  by  the  letters 
of  the  alphabet.  If  there  were  no  decrement  due  to  friction  the 


-Diagram  Representing  Move- 
ment of  Pointer 


expression 


C 


r 


(a 


e) 


d+f) 


4-2 


would  give  the  correct  position  of  the  point  of  rest.  The  positions 
actually  reached  differ  from  those  to  which  the  above  formula 
would  apply  by  multiples  of  the  decrement  k  which  is  approxi- 
mately constant.  If  a  be  taken  as  the  starting  point  the  position 
b  differs  from  that  which  would  be  attained  if  there  were  no  friction 
by  the  constant  fc,  the  position  c  by  twice  that  constant,  the  posi- 
tion d  by  three  times  the  constant,  etc.  If  now  we  average  the 
two  series,  the  one  to  the  right  the  other  to  the  left  for  five  vibra- 
tions, we  obtain  as  the  expression  for  the  point  of  rest  using  the 
corrected  values : 


C  = 


(a 


^ 


16  QUANTITATIVE   CHEMICAL  ANALYSIS 

In  solving  this  expression  the  value  of  the  .constant  k  is  eliminated 
while  if  an  equal  number  of  readings  be  taken  for  the  two  series 
this  is  no  longer  true. 

The  Accurate  Method  of  Weighing.  Having  determined  in 
the  manner  described  the  point  of  rest  of  the  empty  balance,  the 
weight  of  any  substance  can  be  determined  by  placing  it  on  one 
pan  of  the  balance,  and  adding  weights  to  the  other  until  the  point 
of  rest  corresponds  to  that  originally  found.  If  accurately  carried 
out  the  process  is  a  slow  one,  and  may  be  abbreviated  by  an 
equally  exact  interpolation  process,  which  depends  upon  the  fact 
that  the  change  in  the  point  of  rest  is  directly  proportional  to  the 
weight  by  which  it  is  produced.  In  using  this  method  the  unknown 
substance  is  placed  on  the  left  pan  and  weights  added,  using 
milligrams  only,  until  the  point  of  rest  is  not  far  from  that  of  the 
empty  balance.  If  this  point  of  rest  is  to  the  right  of  C  another 
milligram  is  added  to  the  weights  in  the  pan,  and  the  point  of  rest 
again  determined,  or  if  it  is  to  the  left,  one  milligram  is  removed 
and  the  point  of  rest  determined.  The  difference  A  —  B,  in 
which  A  and  B  represent  the  points  of  rest  corresponding  to  the 
lesser  and  the  greater  weights  respectively,  gives  the  deflection 
produced  by  one  milligram.  In  order  to  change  the  point  of  rest 
to  that  of  the  empty  balance  (A  —  C)  -f-  (A  —  B)  mg.  must  be 
added  to  the  lesser  weight.  The  interpolation  method  is  repre- 
sented graphically  on  Fig.  2,  which  shows  the  actual  positions  of  A, 
B  and  C,  on  the  ivory  scale  in  a  specific  case.  It  is  obvious  that 
(12  —  9)  -T-  (12  —  6)  or  0.5  mg.  must  be  added  to  the  weight  which 
gave  the  point  of  rest  A  in  order  to  counterbalance  the  unknown 
substance  in  the  left  pan.  The  value  of  (A  —  B)  is  approximately 
constant,  and  unless  there  are  wide  variations  in  the  load  sustained 
by  the  beam,  may  be  assumed  to  be  exactly  so,  hence,  it  is  often  pos- 
sible to  omit  the  determination  of  either  A  or  B  if  the  proper  con- 
stant has  been  previously  determined.  The  value  of  C  does  not 
usually  differ  greatly  during  the  course  of  a  laboratory  period,  and 
need  only  be  determined  once.  This  method  of  weighing  is  the  most 


THE  METHOD  OF  WEIGHING  17 

accurate  in  use  and  with  experience  is  rapidly  executed.  Under 
favorable  conditions  it  should  be  possible  to  reduce  the  error 
involved  in  weighing  by  this  process  to  one-tenth  of  a  milligram, 
but  this  represents  the  extreme  limit  of  accuracy  which  can  be 
attained  with  the  ordinary  analytical  balance.  If  a  greater  degree 
of  accuracy  is  demanded  a  more  carefully  constructed  "  assay 
balance"  must  be  used,  but  this  cannot  be  employed  for  weights 
which  exceed  5  grams. 

Abbreviations  of  Accurate  Method.  In  all  kinds  of  quantita- 
tive work  it  is  the  percentage  rather  than  the  absolute  error  which 
has  to  be  considered,  and  where  large  amounts  of  material  are  to 
be  weighed  the  above  method  may  be  shortened.  If  we  are  to 
weigh  a  precipitate  of  about  the  magnitude  of  one  gram,  and  weigh 
to  within  one-tenth  of  a  milligram,  the  percentage  error  involved 
will  be  one-hundredth,  which  is  insignificant,  as  compared  with 
the  other  unavoidable  errors  of  most  quantitative  processes,  and 
even  if  the  error  involved  is  a  half  milligram  the  percentage  error 
is  not  excessive.  If,  however,  our  precipitate  weighs  two-tenths 
of  a  gram  an  absolute  error  of  a  half  milligram  cannot  be  safely 
disregarded.  The  abbreviation  referred  to  above  consists  in 
making  a  rough  mental  calculation  of  the  point  of  rest  from  a  mere 
inspection  of  the  movement  of  the  pointer.  It  may  be  further 
noted  that  most  of  the  weighings  made  actually  involve  the  differ- 
ence between  two  weights,  namely,  the  weight  of  the  empty  vessel 
and  that  of  the  vessel  and  substance.  If  the  same  point  of  rest 
is  assumed  for  both  weighings,  the  same  error  will  appear  in  both 
and  the  difference  will  give  the  correct  value  of  the  magnitude 
desired.  The  point  usually  assumed  is  the  center  of  the  scale. 
Hence  the  process  of  weighing  which  may  be  used  in  such  cases 
consists  in  manipulating  the  weights  till  the  pointer  swings  to 
approximately  an  equal  number  of  divisions  on  both  sides  of  the 
center  of  the  scale,  making  the  proper  allowance  for  the  decre- 
ment in  the  amplitude  of  each  vibration.  The  error  involved 
in  this  method  should  not  exceed  three-tenths  of  a  milligram. 


18  QUANTITATIVE  CHEMICAL  ANALYSIS 

Some  judgment  must  be  used  as  to  which  of  these  methods  of 
weighing  should  be  employed,  but  a  fairly  satisfactory  general 
rule  is  to  use  the  more  accurate  method  when  the  quantity  weighed 
was  less  than  three-tenths  of  a  gram. 

The  Weights  Used.  Since  the  results  of  quantitative  proc- 
esses are  usually  expressed  in  terms  of  the  ratio  of  the  substance 
found  to  the  substance  used,  and  since  the  same  set  of  weights  is 
used  to  determine  the  value  of  both  of  these  magnitudes,  the  abso- 
lute value  of  the  standard  or  unit  mass  employed  is  of  no  signifi- 
cance. If  the  weights  used  are  consistent  between  themselves, 
that  is,  if  the  different  pieces  bear  to  each  other  the  exact  relation 
for  which  they  are  used,  no  error  will  appear  in  the  final  result. 
If,  however,  as  in  the  assay  of  gold  and  silver  ores,  the  result  is 
to  be  reported  in  terms  of  the  money  value  per  ton,  the  absolute 
value  of  the  unit  of  weight  employed  is  of  the  greatest  importance. 
The  sets  of  weights  sold  by  firms  of  established  reputation  are 
frequently  sufficiently  accurate  for  most  kinds  of  work,  but  the 
results  obtained  with  them  will  always  be  subject  to  some  uncer- 
tainty until  they  have  been  accurately  tested.  Such  weights 
should  be  handled  with  ivory-tipped  pincers  and  kept  in  a  closed 
box  when  not  in  use.  Platinum  weights  should  not  change  in 
value  even  after  years  of  constant  use,  but  aluminum  weights 
are  subject  to  slight  corrosion  and  must  be  more  carefully  pro- 
tected. 

The  manipulation  of  very  small  weights,  especially  those  below 
5  mg.  in  value,  is  troublesome  and  is  usually  avoided  by  the  use 
of  a  " rider.7'  This  is  a  piece  of  platinum  or  aluminum  wire  bent 
in  such  form  as  to  hang  on  the  beam  of  the  balance,  and  easily 
movable  from  place  to  place  on  the  beam  by  means  of  a  hook. 
If  such  a  rider,  whose  weight  is  exactly  5  mg.,  is  placed  on  the 
beam  of  the  balance  exactly  above  the  point  of  suspension  of  the 
pan  containing  the  weights  it  would  have  the  same  effect  as  the 
addition  of  5  mg.  to  that  pan,  or  if  placed  in  any  position  between 
this  point  and  the  point  of  suspension  of  the  beam  it  would 


THE  METHOD  OF  WEIGHING 


19 


have  an  effect  proportional  to  its  distance  from  ^the  point  of  sus- 
pension of  the  beam.  If  the  beam  is  divided  into  five  equal 
parts  each  division  would  be  equivalent  to  1  mg.  Further  sub- 
division of  these  large  divisions  enables  one  to  add  tenths  of  a  milli- 
gram as  desired. 

The  Calibration  of  Weights.  It  is  often  necessary  to  accu- 
rately calibrate  a  set  of  weights.  This  involves  first  a  determina- 
tion of  the  exact  relations  between  the  different  pieces  composing 
the  set,  and  second  a  reduction  of  the  values  thus  obtained  to  the 
absolute  metric  unit  or  some  other  convenient  standard.  The 
method  can  be  readily  illustrated  by  a  concrete  example.  In  this 
work  the  5  mg.  weight  was  temporarily  adopted  as  a  standard  of 
reference  and  was  found  to  agree  absolutely  with  the  rider  of  the 
balance.  By  comparing  systematically  the  different  pieces  of  the 
set  on  an  assay  balance  the  results  recorded  in  the  accompanying 
table  were  obtained.  In  this  table  the  first  column  represents  the 
marks  on  the  weight  placed  in  the  left  pan  of  the  balance,!  the 
second  column  the  weights  added  to  the  right  pan,  and  the  third 
the  position  of  the  rider  on  the  beam  of  the  balance.  The  figures 


5 

0 

5' 

5 

5 

10 

5 

5 

10 

10 

10' 

10 

0 

10 

10 

20 

10+10* 

0 

20 

20 

50 

20+10+10'  +5 

5.08 

50.08 

50 

100 

50+20+10+10*+5 

5.08 

100.16 

100 

100*. 

100 

0.05 

100.21, 

100.1 

200 

100+100* 

0.05 

200.42 

200.2 

500 

200+100+100*+50+20+10+10*+5 

5.08 

500.95 

500.3 

1000 

500+200+100+100*+50+20+10+10*+5 

5.12 

1001.94' 

1000.7  / 

in  the  fourth  column  represent  a  summation  of  those  in  the  second 
and  third  plus  the  corrections  previously  found,  and  hence  the 
values  of  the  different  weights  in  terms  of  the  5  mg.  weight. 

The  1  gm.  weight  was  next  compared  with  a  standard  metric 
gram  on  an  assay  balance  and  found  to  have  the  value  1.00075. 


20  QUANTITATIVE   CHEMICAL  ANALYSIS 

Multiplying  the  sgries  of  figures  in  the  fourth  column  by  the  factor 
(1.00075  -s-  1.0019),  that  is,  0.9988,  they  were  reduced  to  the  corre- 
sponding values  in  terms  of  the  absolute  metric  units  and  the  results 
which  appear  in  the  last  column  of  the  table  obtained.  The  figures 
which  appear  in  the  second  decimal  place  have  no  significance  in 
analytical  work  and  are  therefore  neglected. 

Correction  for  Buoyancy.  The  apparent  effect  of  gravity  upon 
any  object  which  is  surrounded  by  the  atmosphere  is  less  than 
the  true  effect  by  an  amount  corresponding  to  the  weight  of  the 
volume  of  air  which  it  displaces.  If  the  loads  sustained  by  the 
two  pans  of  the  balance  displace  the  same  volume  of  air,  buoyancy 
affects  both  equally,  but  where  the  object  being  weighed,  and  the 
weights  used  to  counterbalance  it  differ  in  volume,  buoyancy 
affects  the  load  displacing  the  greater  volume  of  air  to  a  greater 
extent  than  the  other,  and  causes  a  corresponding  error.  The 
magnitude  of  this  error  can  be  calculated  from  the  weight  of  a 
unit  volume  of  air,  and  the  difference  between  the  specific  gravities 
of  the  weights  and  object  weighed.  The  correction  is  usually 
much  smaller  than  the  other  unavoidable  errors  of  the  majority 
of  quantitative  processes,  and  unless  an  unusual  degree  of  accuracy 
is  demanded  can  be  safely  disregarded. 

The  Error  Resulting  from  Hygroscopic  Water.  Any  solid 
object,  which  has  not  been  especially  dried  and  maintained  in  an 
atmosphere  which  is  free  from  water  vapor,  retains  a  film  of  hygro- 
scopic water  upon  its  surface.  If  the  surface  presented  is  large 
the  true  weight  of  such  an  object  may  differ  from  the  apparent 
weight,  that  is,  the  weight  determined  under  ordinary  atmospheric 
conditions,  by  several  milligrams;  and  further,  the  difference 
varies  with  the  amount  of  water  in  the  atmosphere.  Alt  ho  this 
film  of  water  can  be  expelled  by  heating  the  object  to  100°  for  a 
few  minutes,  it  is  not  readily  possible  to  entirely  prevent  the  re- 
absorption  of  hygroscopic  water  while  it  is  being  cooled  and 
weighed.  A  15-gm.  crucible,  for  example,  which  has  been  allowed 
to  cool  in  a  desiccator,  and  which  is  weighed  in  a  balance,  the  case 


THE   METHOD   OF  WEIGHING  21 

of  which  contains  a  jar  of  calcium  chloride,  will  frequently  show 
a  gain  of  from  one  to  three-tenths  of  a  milligram  on  long  standing 
on  the  balance  pan.  When  it  is  necessary  to  weigh  accurately 
to  one-tenth  of  a  milligram  this  becomes  one  of  the  most  trouble- 
some difficulties  to  avoid. 

Since  most  weighings  are  made  in  some  form  of  a  container, 
such  as  a  crucible  or  bottle,  the  weight  actually  used  in  the  final 
calculation  represents  the  difference  between  the  weight  of  the 
container  plus  substance  and  the  container,  and  the  error  resulting 
from  the  absorption  of  hygroscopic  water  can  often  be  reduced 
to  negligible  proportions  by  submitting  both  to  exactly  the  same 
conditions  before  weighing.  If,  for  example,  the  empty  crucible 
and  the  crucible  plus  the  substance  to  be  weighed  are  ignited, 
placed  in  a  desiccator  while  still  warm,  allowed  to  stand  for  an 
hour  and  then  weighed  at  once  the  amount  of  hygroscopic  water 
absorbed  by  the  crucible  in  the  two  cases  is  practically  the  same, 
but  not  exactly  so  unless  the  percentage  of  water  vapor  in  the 
atmosphere  has  remained  constant.  The  only  error  to  be  con- 
sidered in  such  a  case  is  that  due  to  the  absorption  of  water  by 
the  substance  itself,  which  can  usually  be  neglected  unless  it  is 
decidedly  hygroscopic.  If  it  is  decidedly  hygroscopic  it  becomes 
necessary  to  use  a  closed  container.  When  the  container  cannot 
be  heated  to  a  temperature  necessary  to  drive  off  all  hygroscopic 
water,  wiping  with  a  dry  cloth  has  to  be  substituted.  When  the 
surface  presented  by  the  container  is  very  large,  variations  in  the 
moisture  content  of  the  air  may  lead  to  errors  which  cannot  be 
neglected.  In  such  cases  it  is  desirable  to  prepare  a  counterpoise 
of  about  the  same  surface  area  as  the  vessel  to  be  weighed,  to 
submit  both  vessels  to  the  same  treatment  before  both  weighings 
and  to  substitute  the  counterpoise  for  some  of  the  weights  employed 
in  both  cases.  It  may  be  assumed  that  variations  in  the  atmos- 
pheric conditions  will  affect  the  amount  of  water  retained  by  the 
two  vessels  to  the  same  extent,  and  that  no  error  from  this  source 
will  appear  in  the  difference  finally  found. 


22  QUANTITATIVE   CHEMICAL  ANALYSIS 

II.   RULES  FOR  THE  USE  OF  THE  BALANCE 

Altho  the  general  facts  and  principles  upon  which  the  use  of  the 
balance  is  based  have  been  presented  in  the  preceding  section, 
there  are  a  number  of  details  of  a  purely  practical  nature  which 
must  be  observed  if  the  balance  is  to  be  maintained  in  good  work- 
ing order.  These  are  elaborated  in  the  form  of  the  series  of  rules 
given  below. 

First,  in  order  to  prevent  wear  of  the  bearings,  and  consequent 
rapid  decrease  in  the  sensitiveness  of  the  balance,  large  weights 
should  never  be  placed  on  or  removed  from  the  balance  pans, 
unless  the  beam-  and  pan-rests  are  in  position;  if  the  weight  being 
added  or  removed  does  not  exceed  100  mg.  the  pan-rests  alone  will 
suffice.  Both  rests  should  always  be  left  in  position  before  leaving 
the  balance. 

Second,  the  floor  of  the  balance  case  and  the  pans  should  be 
kept  perfectly  clean.  If  substances  are  spilled  within  the  case 
they  should  be  brushed  up  at  once  with  a  fine  brush  or  cloth.  . 

Third,  no  solid  substances  except  certain  metals  and  alloys 
should  be  placed  in  contact  with  the  balance  pans.  No  liquids 
of  any  description  should  be  brought  into  the  balance  case  unless 
retained  in  tightly  stoppered  bottles. 

Fourth,  hot  objects  should  be  allowed  to  cool  to  a  temperature 
not  greatly  in  excess  of  the  normal  temperature  of  the  balance 
room  before  being  weighed.  If  this  precaution  is  not  taken  dis- 
turbing air  currents  are  set  up  within  the  balance  case.  For  a  like 
reason  the  slide  of  the  balance  case  should  be  kept  closed  while 
the  movements  of  the  beam  are  being  observed. 

Fifth,  the  weights  should  always  be  handled  with  bone-tipped 
forceps  and  should  be  carefully  protected  from  dust  and  fumes. 

Sixth,  if  the  point  of  rest  of  the  empty  balance  differs  from  ten 
by  more  than  one  unit,  or  if  the  balance  fails  to  behave  properly, 
ask  the  instructor  in  charge  to  make  whatever  adjustments  may 
be  necessary. 


THE  METHOD  OF  WEIGHING  23 

III.   DETAILS   OF   PROCEDURE   FOR  DETERMINATION    OF   POINT 

OF  REST 

Seat  yourself  squarely  in  front  of  the  balance  case  so  that  your 
line  of  vision  is  directly  opposite  the  center  of  the  balance.  Re- 
lease the  beam-rests  by  turning  the  button  at  the  center  of  the 
case,  then  the  pan-rests  by  pressing  the  small  knob  to  the  left, 
next  gently  lower  the  rider  till  it  rests  on  the  end  of  the  beam  and 
allow  it  to  remain  just  long  enough  to  displace  the  pointer  about 
ten  divisions  on  the  ivory  scale,  and  finally  remove  the  rider  and 
permit  the  beam  to  swing  freely.  Take  an  odd  number  of  con- 
secutive readings  (five  are  sufficient)  corresponding  to  the  extreme 
positions  reached  by  the  pointer.  Add  together  the  averages  of 
the  two  sets  of  readings,  one  set  representing  all  the  readings  taken 
on  the  right  of  the  center,  the  other  all  the  readings  taken  on  the 
left  of  the  center,  and  divide  the  sum  by  two.  This  gives  the 
point  of  rest  of  the  empty  balance.  Repeat  the  determinations 
till  results  are  obtained  whose  extreme  differences  do  not  exceed 
two-tenths  of  a  division. 

IV.   DETAILS  OF  PROCEDURE  FOR  THE  DETERMINATION 
OF  THE  WEIGHT  OF  A  WATCH  GLASS 

Elaborate  Method.  Hold  a  clean  watch  glass  over  a  gauze 
heated  by  the  flame  of  a  burner  until  it  is  decidedly  hot  to  the 
touch,  then  place  on  a  clean  support  inside  a  desiccator  and  allow 
to  cool  for  twenty  minutes.  Transfer  the  glass  by  means  of  clean 
"  dry  pincers  to  the  left  pan  of  the  balance  and  add  in  regular 
succession  weights  of  decreasing  value  to  the  right  pan  until  the 
correct  weight  is  determined  to  within  10  mg.  if  the  balance  is 
provided  with  a  10-mg.  rider,  and  to  within  5  mg.  if  it  is  provided 
with  a  5-mg.  rider.  Next  vary  the  position  of  the  rider  on  the 
right  arm,  placing  it  at  points  corresponding  to  entire  milligrams, 
until  the  weight  is  found-  to  within  1  mg.  Finally  determine 
accurately  the  point  of  rest,  first,  with  the  rider  in  the  position 


24  QUANTITATIVE  CHEMICAL  ANALYSIS 

which  makes  the  total  weights  used  slightly  less,  and  second  that 
which  makes  the  total  weights  used  slightly  greater  than  that  of 
the  watch  glass.  These  relations  can  be  determined  by  noting 
whether  the  pointer  swings  decidedly  to  the  right  or  the  left  as 
the  changes  are  made. 

Let  A  represent  the  point  of  rest  found  with  the  lesser  weight, 
B  that  found  with  the  greater  weight,  and  C  the  point  of  rest  of 
the  empty  balance.  Calculate  the  correction,  expressed  in  milli- 
grams, to  be  added  to  the  lesser  weight  necessary  to  shift  the  point 
of  rest  from  A  to  C  by  dividing  (A  —  C)  by  (A  —  -5),  and  add 
this  correction  to  the  lesser  weight. 

Verify  the  accuracy  of  the  result  by  adding,  by  means  of  the 
rider,  the  fraction  of  a  milligram  calculated  to  be  necessary  and 
again  determine  the  point  of  rest.  If  the  work  has  been  accurately 
carried  out,  and  if  the  balance  is  properly  constructed  and  ad- 
justed, the  points  of  rest  obtained  should  not  differ  from  that  of 
the  empty  balance  by  more  than  two-tenths  of  a  division  of  the 
ivory  scale. 

Make  a  permanent  record  of  the  weight  thus  obtained  in  the 
laboratory  notebook,  in  which  all  weighings  and  the  data  upon 
which  they  are  based  should  be  recorded  when  obtained.  Dis- 
regard all  figures  beyond  the  fourth  decimal  place. 

Abbreviation  of  the  Method  Outlined.  In  subsequent  work 
this  method  of  weighing  may  often  be  abbreviated.  Where  the 
weight  actually  determined  is  the  difference  between  the  weight 
of  the  containing  vessel  and  the  weight  of  that  vessel  plus  another 
substance,  the  point  of  rest  of  the  empty  balance  may  be  assumed 
to  be  ten.  Where  the  magnitude  of  the  mass  weighed  is  not  less 
than  0.25  gm.  the  accurate  determination  of  the  points  of  rest  may 
be  omitted  and  the  weight  determined  with  sufficient  accuracy 
by  changing  the  position  of  the  rider  on  the  beam  until  the  pointer 
swings  to  approximately  the  same  distance  on  either  side  of  the 
point  of  rest  of  the  empty  balance,  making  a  slight  allowance  for 
the  decrease  in  the  value  of  each  successive  vibration. 


THE  METHOD  OF  WEIGHING  25 

V.   DETAILS  OF  PROCEDURE  FOR  CALIBRATION  OF  A  SET 
OF  WEIGHTS 

Determine  the  relations  between  the  different  pieces  composing 
the  set  using  the  procedure  outlined  on  page  19.  It  is  not  neces- 
sary to  reduce  the  results  to  the  absolute  metric  standard. 

VI.   QUESTIONS  AND  PROBLEMS.     SERIES  1 

/  1.  The  right  arm  of  a  balance  has  a  length  of  150.1  mm.,  the  left  arm 
150  mm. ;  the  apparent  weight  of  a  crucible  placed  in  the  left  pan  is  10.032 
gm.,  what  is  its  true  weight? 

2.  What  error  would  result  in  weighing  a  0.3  gm.  precipitate  in  the  crucible 
referred  to  above  if,  first,  both  empty  crucible  and  crucible  plus  precipitate 
are  weighed  on  the  left  pan,  and  second,  if  the  crucible  is  weighed  on  the 
right  pan  and  the  crucible  plus  precipitate  on  the  left  pan? 

3.  Show  that  no  error  is  involved  in  weighing  a  precipitate  if  the  point  of 
rest  of  the  empty  balance  is  not  actually  determined,  provided  the  same 
value  is  assumed  in  weighing  both  empty  crucible  and  the  crucible  plus  pre- 
cipitate. 

4.  The  right  arm  of  a  balance  is  divided  into  12  equal  divisions,  the  appar- 
ent weight  of  a  crucible  determined  with  it  is  10.0582,  it  is  subsequently 
found  that  the  rider  used  weighed  10  mg.,  what  is  the  true  weight  of  the 
crucible? 

5.  The  weight  of  a  balance  beam  is  350  gm.,  its  total  length  200  mm.,  and 
the  pointer  attached  to  it  has  a  length  of  180  mm.;  if  one  milligram  causes  a 
deflection  of  2  mm.  at  the  end  of  this  pointer,  what  is  the  position  of  the  center 
of  gravity  with  respect  to  the  point  of  suspension? 

6.  What  error  results  from  failure  to  correct  for  buoyancy  in  weighing  a 
10-gm:  porcelain  crucible,  assuming  that  brass  weights  with  a  specific  gravity 
of  8.33  are  used,  that  the  specific  gravity  of  porcelain  is  2.14  and  that  one 
liter  of  air  weighs  1.2  gm.? 

7.  A  crucible  is  found  to  weigh  10.0542  gm.  when  placed  on  the  right-hand 
pan  of  a  balance  and  10.058  gm.  when  placed  on  the  left-hand  pan;  what  is  f 
the  true  weight  of  the  crucible?     If  the  total  length  of  the  beam  is  180  mm., 
what  is  the  difference  in  the  lengths  of  the  two  arms? 


CHAPTER  III 

PREPARATION   OF  THE   SUBSTANCE   FOR  ANALYSIS 

Theory  of  Sampling.  The  amount  of  substance  actually  em- 
ployed in  making  a  quantitative  analysis  is  comparatively  small, 
and  the  result  obtained  is  of  but  little  value  unless  the  portion 
actually  used  accurately  represents  the  average  composition  of 
the  entire  mixture.  In  the  analysis  of  gases  and  liquids  homo- 
geneous mixtures  are  very  easily  obtained  by  a  slight  amount  of 
stirring,  but  in  the  analysis  of  solid  mixtures  it  is  usually  neces- 
sary to  prepare  a  "sample."  The  difficulties  which  arise  in 
preparing  a  representative  sample  of  a  solid  mixture  result  from 
differences  in  size  and  lack  of  uniformity  in  the  distribution  of  the 
different  constituents,  and  from  differences  in  the  hardness  and 
the  specific  gravity  of  these  constituents.  The  general  method 
of  procedure  in  sampling  a  non-homogeneous  solid,  whether  it 
represents  a  carload  or  a  few  pounds  is  essentially  the  same.  It 
involves  removing  and  setting  aside  according  to  a  uniform  plan 
a  fractional  part  of  the  total  amount,  reducing  the  portion  set 
aside  to  a  finer  state  of  division,  mixing  thoroughly,  and  repeating 
this  cycle  of  operations  until  a  sample  of  such  fineness  is  obtained 
that  the  small  amount  actually  weighed  out  represents  the  entire 
original  mass.  The  fundamental  principle  which  must  be  kept 
in  mind  is  that  the  fineness  to  which  the  sample  is  crushed  at  each 
cycle  must  be  such  that  the  ratio  between  the  size  of  the  sample 
and  the  size  of  the  largest  particle  is  sufficiently  large.  The  size 
of  the  largest  particle  must  be  so  small  that  the  addition  of  one 
such  particle  to  the  portion  which  has  been  selected  does  not 
change  the  average  composition  of  the  mixture  by  an  appreciable 

26 


PREPARATION  OF  THE   SUBSTANCE   FOR  ANALYSIS       27 

amount.  Many  factors  have  to  be  considered  in  deciding  upon 
the  smallest  ratio  which  can  be  safely  adopted;  that  of  1000  : 1  is 
frequently  used. 

Methods  of  Selection.  The  simplest  method  of  selecting  a 
fractional  part  of  the  mixture  is  to  turn  over  the  entire  mass  with 
a  shovel  or  spoon,  and  set  aside  every  tenth,  fifth,  or  second  shovel 
or  spoonful.  Another  method  is  to  distribute  the  entire  mass  in 
the  form  of  a  cone-shaped  pile,  flatten  the  pile  slightly,  and  remove 
a  sector  representing  one-quarter  or  one-half  of  the  pile;  it  can  be 
assumed  that  the  large  and  small  particles  and  the  light  and  heavy 
particles  are  distributed  symmetrically  with  respect  to  the  central 
axis  of  such  a  cone.  A  large  number  of  mechanical  devices,  which 
automatically  separate  a  fractional  part  of  all  the  material  passed 
through  them,  are  used  where  the  sample  is  large. 

Methods  of  Powdering.  A  great  variety  of  grinding  or  shred- 
ding machines,  which  are  especially  adapted  to  the  nature  of 
different  classes  of  materials,  are  in  use.  Altho  the  grinding 
parts  of  such  machines  are  made  of  hardened  steel,  appreciable 
amounts  of  iron  are  added  to  the  sample  during  the  grinding 
process  if  the  sample  contains  constituents  whose  hardness  ap- 
proaches that  of  steel.  This  is  usually  neglected  in  commercial 
work,  but  cannot  be  tolerated  in  many  lines  of  scientific  work.  In 
such  cases  the  sample  must  be  pulverized  by  hand  by  means  of  a 
mortar  and  pestle  which  are  made  of  agate.  It  is  sometimes 
advantageous  to  separate  out  the  coarse  from  the  fine  particles 
during  the  grinding  process;  but  since  certain  constituents  of  the 
mixture  may  be  more  easily  reduced  than  others,  none  of  the 
sample  can  be  rejected,  that  is,  the  entire  sample  must  be  made  to 
pass  thru  the  sieve  used. 

Methods  of  Mixing.  Mixing  is  best  performed  by  placing  the 
mass  in  a  cylindrical  vessel,  which  is  then  carefully  corked  and 
rotated  by  means  of  a  motor.  The  same  result  can  be  obtained 
more  slowly  by  hand  rotation.  Another  method  consists  in  plac- 
ing the  sample  on  a  large  piece  of  rubber  "  sampling-cloth "  and 


28 


QUANTITATIVE  CHEMICAL  ANALYSIS 


rolling  the  contents  toward  the  center  by  raising  successively  the 
opposite  corners  of  the  cloth.  Mixing  and  grinding  can  be  ef- 
fected simultaneously  by  means 
of  the  small  "ball  mill'7  repre- 
sented in  Fig.  5.  It  consists 
of  a  porcelain  jar,  which  con- 
tains in  addition  to  the  sample 
a  large  number  of  porcelain 
balls.  When  closed  and  ro- 
tated these  rapidly  reduce  the 
sample  to  a  fine  homogeneous 
mixture. 


Fig.  5.  — Ball  Mill 


The  Moisture  Content  of  the  Sample.  All  solid  substances 
contain  at  least  appreciable  amounts  of  hygroscopic  water  unless 
previously  dried.  If  the  percentage  is  large  the  fine  particles  tend 
to  stick  together  and  may  make  it  impossible  to  powder  and  mix 
the  sample  properly.  Frequently  a  mass  which  seems  to  be  fairly 
dry  becomes  moist  and  sticky  as  soon  as  it  is  roughly  powdered, 
since  water  is  sometimes  held  within  the  interior  of  the  larger 
masses. 

The  chemist  is  usually  expected  to  report  results  on  the  basis 
of  the  mixture  actually  received.  If  he  dries  the  mixture  sub- 
mitted to  him  in  order  to  make  it  possible  to  prepare  a  representa- 
tive sample  the  results  obtained  will  not  represent  the  composition 
of  the  original  mixture.  In  such  cases  it  becomes  necessary  to 
save  out  a  sufficient  amount  of  the  original  mixture  to  permit  of 
an  accurate  determination  of  the  water  present,  and  to  multiply 
the  results  of  the  analysis  by  the  difference  between  100  and  the 
percentage  of  water  found  in  order  to  report  the  percentages 
present  in  the  original  mixture. 

If  the  sample  contains  a  small  amount  of  hygroscopic  water  only 
it  is  preferable  not  to  dry  it,  for  since  all  finely  divided  substances 
are  at  least  appreciably  hygroscopic  it  is  often  difficult  to  preserve 
such  samples  and  to  weigh  them  out  accurately. 


PREPARATION  OF  THE  SUBSTANCE  FOR  ANALYSIS       29 


Methods  of  Drying.  Hygroscopic  water  is  usually  determined 
by  drying  the  sample  in  an  oven  (see  Chapter  IX)  which  is  kept 
at  a  temperature  of  105°.  This  method  cannot  be  used  where  the 
sample  loses  chemically  combined 
water,  or  undergoes  other  changes 
at  this  temperature.  In  such  cases, 
dehydration  can  be  effected  by  the 
use  of  a  desiccator  similar  to  the  one 
represented  in  Fig.  6.  It  consists  of 
a  glass  vessel  provided  with  a  tightly 
fitting  cover,  and  containing  some 
substance,  such  as  strong  sulfuric 
acid  or  calcium  chloride,  which  is  a 
good  absorbent  of  water.  The  gen- 
eral theory  of  its  use  will  be  dis- 
cussed in  Chapter  X. 

Still  another  device  which  some- 


Fig.  6.  —  Desiccator 


times  becomes  necessary  is  to  absorb  the  water  by  means  of  a  filter 
paper  or  a  porous  plate.  The  finely  powdered  substance  is  manip- 
ulated by  means  of  a  spatula  in  such  a  manner  that  fresh  portions 
of  the  mass  are  constantly  brought  into  contact  with  the  plate  or 
paper;  the  capillary  action  of  these  agents  gradually  absorbs  trie 
adhering  water. 


CHAPTER  IV 

THE   PROPERTIES   OF   SOLUTIONS   AND   THE  ELECTROLYTIC 
DISSOCIATION   THEORY 

The  Possible  Kinds  of  Solutions.  Solutions  are  defined  as 
homogeneous  mixtures  whose  composition  can  undergo  continuous 
variation  between  certain  definite  limits.  Such  mixtures  repre- 
senting all  three  states  of  aggregation  are  known.  All  substances 
in  the  gaseous  state  are  miscible  with  each  other  in  any  proportions 
whatever.  In  the  liquid  state  the  possibilities  are  limited;  certain 
pairs  of  liquids,  such  as  alcohol  and  water,  are  capable  of  forming 
a  continuous  series  of  homogeneous  mixtures;  others,  such  as 
ether  and  water,  are  mutually  miscible  to  a  limited  extent  only. 
In  the  solid  state  the  possibilities  are  still  more  limited  and  it  was 
only  comparatively  recently  that  the  existence  of  " solid  solutions" 
was  recognized.  Instances  in  which  two  solids  are  miscible  in  any 
proportions  whatever  are  known,  but  usually  solids  are  soluble 
in  each  other  to  a  limited  extent  only.  Solids  which  are  closely 
related  to  each  other  crystal lographically,  that  is,  which  are  iso- 
morphous,  usually  form  solid  solutions  with  one  another.  Many 
solid  mixtures  which  appear  to  be  homogeneous  can  be  shown  by 
examination  with  a  microscope  to  be  very  finely-grained  conglom- 
erates of  the  constituent  solids,  and,  therefore,  are  not  true  solutions. 

Substances  existing  in  different  states  of  aggregation  are  often 
able  to  form  solutions  with  each  other.  Gases  are  frequently 
soluble  in  both  liquids  and  solids  up  to  a  certain  extent;  liquids 
sometimes  dissolve  in  solids  to  a  limited  extent,  and  solids  are 
often  soluble  in  liquids.  In  dealing  with  solutions  of  all  classes  it 
is  customary  to  designate  the  substance  present  in  relatively  large 
amount  as  the  " solvent"  and  the  substance  present  in  relatively 

30 


PROPERTIES  OF  SOLUTIONS  31 

small  amount  as  the  dissolved  substance  or  "solute.'1  If  the  two 
constituents  of  the  solution  are  miscible  in  all  proportions  either 
may  be  the  solvent  or  the  solute  according  to  the  proportions 
represented  in  the  mixture  concerned. 

Solutions  of  Gases  in  Liquids.  The  solubility  of  a  gas  in  a 
liquid  is  usually  expressed  in  terms  of  the  volume  of  gas,  measured 
under  standard  conditions  of  temperature  and  pressure,  dissolved 
by  a  unit  volume  of  the  liquid.  The  gases  which  are  most  fre- 
quently dealt  with  in  quantitative  work  are,  with  the  exception  of 
ammonia  and  the  halogen  acids,  but  slightly  soluble  in  water,  or 
aqueous  solutions  which  do  not  act  upon  the  gas  chemically. 
With  one  or  two  exceptions  only,  the  solubility  of  a  gas  in  a  liquid 
is  decreased  by  increasing  the  temperature.  The  amount  of  gas 
dissolved  by  a  liquid  increases  in  direct  proportion  to  the  pressure 
of  that  gas  in  contact  with  the  liquid  except  in  those  cases  in  which 
the  solubility  is  very  great.  The  complete  saturation  of  a  liquid 
with  a  gas  requires  intimate  contact  of  the  two  components  for 
some  time,  and  is  not  usually  attained  unless  a  stream  of  gas  is 
permitted  to  pass  through  the  liquid,  or  unless  the  liquid  is  shaken 
with  an  excess  of  the  gas  in  a  closed  vessel. 

Solutions  of  Solids  in  Liquids.  The  solubility  of  a  solid  in  a 
liquid  is  expressed  either  in  terms  of  the  number  of  grams  of  solid 
which  can  be  dissolved  in  a  liter  of  the  pure  liquid,  or  of  the  number 
of  grams  of  solute  present  in  a  liter  of  the  saturated  solution.  The 
weight  of  solute  present  in  a  unit  volume  of  any  solution,  whether 
saturated  or  not,  is  known  as  the  "  concentration/7  Increasing 
the  temperature  usually  increases  the  solubility  of  solids  in  liquids, 
altho  the  increment  per  degree  is  often  small;  a  relatively  small 
number  of  cases  are  known  in  which  the  solubility  decreases  with 
increasing  temperature.  The  effect  of  pressure  upon  the  solu- 
bility of  solids  is  small  and  unless  the  differences  concerned  amount 
to  a  hundred  atmospheres  can  be  neglected. 

The  Speed  of  Solution  of  Solids  in  Liquids.  The  rate  at 
which  a  solid  dissolves  in  a  liquid  depends  primarily  upon  the  rate 


32  QUANTITATIVE  CHEMICAL  ANALYSIS 

at  which  the  particles  of  solid  are  taken  up  by  the  liquid,  and  the 
rate  at  which  the  dissolved  particles  pass  away  from  the  immediate 
neighborhood  of  the  solid  and  diffuse  into  the  surrounding  liquid. 
Both  of  these  factors  depend  upon  the  specific  natures  of  the  solid 
and  liquid  concerned,  and  upon  the  temperature  and  concentra- 
tion of  the  solution  with  respect  to  the  dissolved  salt.  Increasing 
the  temperature  increases  both  the  rate  at  which  the  solid  body  is 
taken  up  and  the  rate  at  which  the  dissolved  particles  diffuse  into 
the  surrounding  liquid.  The  rate  of  diffusion  is  further  directly 
proportional  to  the  difference  between  the  concentration  of  the 
solution  with  respect  to  the  dissolved  salt  at  any  two  points  in  the 
solution.  Further,  the  amount  of  surface  of  the  solid  as  compared 
with  the  volume  of  liquid  to  be  saturated  and  the  rate  at  which  the 
concentrations  of  different  portions  of  the  solution  are  equalized 
thru  mechanical  agencies  greatly  affect  the  rate  at  which  saturation 
of  the  solution  is  effected. 

It  is  apparent  that  wherever  it  is  desired  to  dissolve  a  given 
amount  of  solid  rapidly  the  latter  should  be  reduced  to  a  fine  state 
of  division  in  order  that  the  extent  of  surface  presented  shall  be 
as  large  as  possible,  that  the  temperature  be  as  high  as  the  other 
conditions  of  the  experiment  permit,  and  that  the  solid  and  liquid 
be  agitated  violently. 

Supersaturated  Solutions.  Altho  the  rate  at  which  a  solid 
is  dissolved  by  a  liquid  decreases  as  the  concentration  of  the 
resulting  solution  increases,  and  becomes  zero  as  soon  as  the 
solution  has  attained  a  certain  maximum  concentration,  it  is 
possible,  under  certain  conditions,  to  prepare  solutions  which 
contain  more  than  the  normal  quantity  of  dissolved  solute;  such 
solutions  are  then  designated  as  "  supersaturated. "  Supersatu- 
rated solutions  usually  result  when  a  solvent  is  saturated  with  a 
solute  at  a  temperature  at  which  the  solubility  is  greater  and  the 
temperature  slowly  changed  to  that  at  which  the  solubility  is  less; 
or,  where  the  solid  is  generated  in  the  solvent  as  the  result  of 
changes  in  the  composition  of  the  liquid.  The  excess  of  dissolved 


PROPERTIES  OF  SOLUTIONS  33 

solute  usually  separates  out  from  such  solutions  on  standing, 
especially  if  the  mixture  is  agitated. 

Effect  of  Size  of  Particles  on  Solubility  of  Solids.  The  size  of 
the  solid  particles  in  contact  with  the  solvent  affects  not  only  the 
rate  at  which  the  solid  dissolves  but,  in  some  cases  at  least,  affects 
the  actual  value  of  the  solubility  constant.  This  was  clearly 
shown  through  a  series  of  experiments*  on  the  solubility  of  gypsum 
(CaS04  •  2  H20)  and  barium  sulphate  in  water.  Solutions  which 
had  been  thoroughly  saturated  thru  long  contact  with  particles 
of  gypsum  of  moderate  size  were  found  to  show  a  decided  increase 
in  concentration  as  soon  as  a  small  amount  of  more  finely  divided 
particles  were  added;  on  long  standing,  however,  the  very  fine 
particles  all  disappeared,  and  the  solubility  constant  attained  its 
former  magnitude.  Solutions  saturated  with  particles  whose 
average  diameter  was  0.002  mm.  were  found  to  contain  2.085  gin. 
of  calcium  sulfate  per  liter;  if  saturated  with  particles  whose 
average  diameter  was  0.0003  mm.  the  concentration  corresponded 
to  2.476  gm.  per  liter,  that  is,  decreasing  the  size  of  the  solid 
particles  from  0.002  to  0.0003  mm.  increased  the  solubility  by 
about  nineteen  per  cent.  Further  experiments  showed  that  with 
solid  particles  whose  average  diameters  equaled  or  exceeded 
0.002  mm.  the  solubility  value  remained  constant  and  was  there- 
fore designated  as  the  " normal  solubility";  if  the  particles  con- 
cerned were  less  than  0.002  mm.  in  diameter  the  solubility  value 
exceeded  the  normal  but  gradually  attained  the  normal  value,  and 
the  very  fine  particles  gradually  disappeared.  Experiments  with 
barium  sulfate  gave  still  more  striking  results.  When  precipitated 
from  a  boiling  solution  the  particles  of  salt  showed  an  average 
diameter  of  0.0018  mm.  and  gave  a  normal  solubility  of  0.0023  gm. 
per  liter;  when  the  particles  of  precipitate  were  reduced  to  0.0001 
mm.  the  solubility  was  increased  to  0.00415  gm.  per  liter  and  with 
the  naturally  occurring  salt,  reduced  to  a  still  finer  state  of  division, 
the  solubility  reached  0.00618  gm.  per  liter. 

*  Hulett,  Zeitschrift  fur  physikalische  Chemie,  37,  385  (1901). 


34  QUANTITATIVE   CHEMICAL  ANALYSIS 

These  facts  explain  the  well-known  phenomenon  that  particles 
of  a  precipitate  which  are  too  small  to  be  retained  by  a  filter  are 
often  retained  on  the  same  filter  after  they  have  been  allowed  to 
remain  in  contact  with  the  solution  for  some  time.  It  is  probable 
that  there  is  a  tendency  for  all  finely  divided  substances  in  contact 
with  their  saturated  solutions  to  increase  the  size  of  their  particles 
up  to  a  certain  minimum,  and  for  the  resulting  saturated  solutions 
to  attain  a  certain  normal  solubility.  If  this  is  generally  true  all 
solutions  which  have  been  saturated  with  a  solid,  some  of  the 
particles  of  which  are  below  the  normal  size,  are  supersaturated 
with  respect  to  the  particles  which  exceed  the  normal  size,  and  on 
standing  some  of  the  dissolved  substance  should  be  deposited  upon 
these  large  particles;  further,  since  the  solution  would  then  be 
undersaturated  with  respect  to  those  particles  which  are  smaller 
than  the  normal  size,  these  should  pass  into  solution.  The  total 
effect  should  be  the  gradual  disappearance  of  all  particles  whose 
size  is  below  the  normal.  Changes  of  this  kind  are  found  to  take 
place  much  more  rapidly  as  the  temperature  of  the  mixture  is 
increased. 

The  Molecular  Weights  of  Dissolved  Substances.  It  was 
first  shown  by  Van't  Hoff  in  1886  that  a  remarkable  analogy  exists 
between  dissolved  and  gaseous  substances.  He  was  able  to  show 
from  the  data  available  at  that  time  that  the  " osmotic  pressure"* 
exerted  by  a  substance  dissolved  in  a  liquid  was  directly  propor- 
tional to  the  concentration  and  to  the  absolute  temperature; 
further,  that  the  osmotic  pressure  of  such  a  solution  was  exactly 
equal  to  the  gaseous  pressure  which  the  solute  should  exert,  if  it 
was  vaporized,  and  if  the  vapor  occupied  a  space  equal  to  the 
volume  of  the  solution  concerned.  The  validity  of  these  con- 
clusions has  been  tested  by  more  recent  investigators,  and  so  far 

*  The  student  should  consult  some  modern  book  on  Theoretical  Chemis- 
try, or  the  first  volume  of  Stieglitz'  "  Qualitative  Analysis,"  for  an  explana- 
tion of  this  term  and  for  a  further  elaboration  of  much  of  the  matter  which 
follows. 


PROPERTIES  OF   SOLUTIONS  35^ 

as  solutions  of  moderate  concentration  are  concerned,  sufficiently 
confirmed.  They  render  it  almost  necessary  to  assume  that  the 
hypothesis  of  Avogadro  is  as  valid  for  dissolved  substances  as  for 
gases,  and  hence  Van't  Hoff  was  led  finally  to  the  conclusion  that 
equal  volumes  of  solutions  of  different  substances,  which  give 
equal  osmotic  pressures,  at  the  same  temperature,  contain  the 
same  number  of  molecules. 

The  most  important  application  of  these  conclusions  was  the 
calculation  of  the  molecular  weights  of  dissolved  substances  from 
determinations  of  the  osmotic  pressures  of  solutions  containing 
them.  Owing  to  the  practical  difficulties  which  arise  in  the  deter- 
mination of  osmotic  pressures,  certain  physical  properties  which 
are  related  to  osmotic  pressure,  such  as  the  changes  in  the  vapor 
pressure  of  the  solvent,  and  in  the  boiling  or  freezing  point  of  the 
solution,  have  been  more  generally  used  for  the  determination  of 
the  molecular  weights  of  dissolved  substances.  When  these 
methods  were  applied  to  certain  classes  of  solutions,  especially  to 
dilute  aqueous  solutions  of  strong  acids,  of  strong  bases,  and  of 
salts  in  general,  the  molecular  weights  obtained  were  less  than  the 
values  usually  assigned  to  these  substances,  in  many  cases  ap- 
proximately one-half  or  one-third  of  these  values.  Van't  Hoff  was 
unable  to  explain  these  discrepancies. 

Development  of  the  Electrolytic  Dissociation  Theory.  In 
1887  Arrhenius  noted  the  fact  that  when  osmotic  pressure  methods 
were  used  for  the  determination  of  molecular  weights,  normal 
values  were  obtained  for  those  solutions  which  did  not  conduct 
electricity,  whereas  abnormally  low  results  were  obtained  with  all 
solutions  which  were  good  conductors.  It  had  been  already  shown 
by  Faraday  that  the  passage  of  an  electric  current  through  a 
solution  w^as  always  associated  with  the  decomposition  of  the 
solute  into  two  products,  one  of  which  separated  at  the  negative 
pole  or  cathode,  and  the  other  at  the  positive  pole  or  anode;  and 
further,  that  the  amount  of  electricity  transmitted  was  directly 
proportional  to  the  weights  of  either  of  the  decomposition  products 


36  QUANTITATIVE  CHEMICAL  ANALYSIS 

formed.  These  facts  suggested  to  Arrhenius  the  "  Electrolytic 
Dissociation  Theory. " 

According  to  this  theory  all  substances  which  form  solutions 
capable  of  conducting  an  electric  current,  and,  therefore,  desig- 
nated as  "  electrolytes,"  do  not  exist  in  such  solutions  in  the  form 
of  the  original  molecules,  but  in  part  at  least  as  "  dissociation 
products.'7  These  products  are  designated  as  "ions/'  or  more 
specifically  as  "cations"  or  "anions/'  according  to  whether  they 
separate  at  the  cathode  or  anode  during  the  passage  of  an  electric 
current  through  the  solution.  The  ions  are  either  simple  elements 
or  combinations  of  elements  charged  with  large  amounts  of  elec- 
tricity, each  cation  with  a  definite  amount  of  positive  electricity, 
and  each  anion  with  an  equal  amount  of  negative  electricity,  or 
with  some  simple  multiple  of  that  amount. 

According  to  these  assumptions  the  abnormally  low  results 
obtained  for  the  molecular  weights  of  electrolytes  is  a  necessary 
consequence  of  the  fact  that  such  solutions  contain  a  greater 
number  of  ultimate  particles,  that  is  ions,  capable  of  affecting  the 
osmotic  pressure  of  the  solution  than  would  be  present  if  the  solu- 
tion was  undissociated.  Such  solutions  are  conductors  because 
the  positively  charged  cations  are  attracted  by  the  negatively 
charged  cathode  and  repelled  by  the  positively  charged  anode, 
while  the  negatively  charged  anions  are  attracted  by  the  positively 
charged  anode  and  repelled  by  the  negatively  charged  cathode. 
These  attractions  and  repulsions  cause  the  cations  to  migrate 
toward  the  cathode,  and  the  anions  toward  the  anode,  that  is, 
cause  a  flow  of  electricity  through  the  solution.  When  the  ions 
reach  the  surfaces  of  the  electrodes  they  lose  their  charges,  which 
change  materially  affects  their  chemical  and  physical  properties, 
and  is  the  cause  of  the  phenomenon  of  "electrolysis." 

Composition  of  the  Ions.  The  probable  composition  of  the 
ions  which  are  present  in  a  solution  of  an  electrolyte  can  usually 
be  inferred  from  the  composition  of  the  substances  which  separate 
at  the  electrodes  during  electrolysis.  When  a  solution  of  hydro- 


PROPERTIES  OF  SOLUTIONS  37 

chloric  acid  is  electrolyzed  gaseous  hydrogen  separates  at  the 
cathode  and  chlorine  at  the  anode.  The  simplest  assumption 
which  can  be  made  is  that  such  a  solution  contains  positively 
charged  hydrogen  ions  and  negatively  charged  chlorine  ions;  the 
hydrogen  atoms,  which  result  from  the  loss  of  positive  charges  by 
two  hydrogen  ions,  unite  to  form  a  molecule  of  hydrogen,  and  the 
chlorine  atoms,  which  result  from  the  loss  of  negative  charges  by 
two  chlorine  ions,  unite  to  form  a  molecule  of  chlorine.  Since 
solutions  of  all  soluble  chlorides  yield  chlorine  during  electrolysis 
it  is  probable  that  all  such  solutions  contain  simple  chlorine  ions. 
When  a  solution  of  a  strong  base,  such  as  potassium  hydroxide, 
is  electrolyzed  hydrogen  is  liberated  at  the  cathode  and  oxygen  at 
the  anode.  It  is  probable  that  the  solution  contains  positively 
charged  potassium  ions  and  negatively  charged  ions  having  the 
formula  HO.  The  metallic  potassium  which  first  separates  at  the 
cathode  at  once  reacts  with  water  to  form  hydrogen  and  more 
potassium  hydroxide;  the  negatively  charged  HO  ions  cannot 
exist  independent  of  this  charge,  and  unite  to  form  water  and 
molecular  oxygen.  All  hydroxides  yield  solutions  containing  these 
ions.  When  a  solution  of  copper  sulfate  is  electrolyzed,  metallic 
copper  separates  at  the  cathode,  and  oxygen  at  the  anode  and  the 
solution  becomes  acid.  It  seems  probable  that  the  solution  con- 
tains positively  charged  copper  ions  and  negatively  charged  ions 
of  the  formula  S04;  the  former  yield  metallic  copper  at  the  cathode, 
but  as  the  latter  cannot  exist  independent  of  their  negative  charge 
they  decompose  and  unite  with  water,  forming  oxygen  and  sulfuric 
acid,  which  in  turn  gives  hydrogen  ions  and  S04  ions. 

A  more  careful  study  of  the  subject,  by  methods  which  need  not 
be  considered  here  shows  that  the  dissociation  of  even  simple 
electrolytes  may  be  a  more  complex  process  than  the  foregoing 
statements  suggest.  It  is  known  for  example,  that  solutions  of 
sulfates  contain  ions  of  the  formula  HSO4,  in  addition  to  SO4  ions, 
also  that  phosphates  yield  ions  of  the  formula  H2P04,  HP04  and 
P04.  Further,  certain  metallic  ions  show  a  decided  tendency  to 


38  QUANTITATIVE  CHEMICAL  ANALYSIS 

unite  with  other  groups  of  elements  such  as  H20,  NH3,  C12  and 
(CN)2. 

In  order  to  designate  the  various  ions,  symbols  which  represent 
not  only  their  chemical  composition  but  also  the  number  and 
character  of  the  charges  which  they  carry  are  used.  The  charge 
carried  by  the  hydrogen  ion  is  chosen  as  the  standard  of  comparison 
and  represented  by  a  single  +  sign  written  above  the  symbol,  ions 
which  carry  double  this  amount  of  positive  charge  are  represented 
by  the  proper  symbol  with  the  +  sign  written  twice.  Similarly, 
ions  which  carry  negative  charges  equal  to  the  positive  charge  of 
the  hydrogen  ion  are  represented  by  the  proper  symbol  with  a 
single  —  sign  written  above  it,  those  which  carry  twice  this  amount 
of  charge  show  the  —  sign  written  twice. 

Factors  Affecting  the  Dissociation  of  Electrolytes.  Since  elec- 
tricity is  carried  through  a  solution  by  the  ions,  not  by  the  un- 
dissociated  molecules  which  it  contains,  its  "conductivity,"  that 
is  its  efficiency  as  a  conductor,  is  a  measure  of  the  extent  to  which 
the  electrolyte  is  dissociated.  In  comparing  the  conductivities 
of  solutions,  the  relations  are  greatly  simplified  if  concentrations 
are  expressed  in  terms  of  gram  molecules  or  "moles"  per  liter, 
that  is,  if  the  weight  of  solute  per  liter  is  divided  by  the  molecular 
weight  of  the  solute  concerned. 

When  the  conductivities  of  solutions,  which  contain  the  same 
number  of  moles  of  various  electrolytes  per  liter,  are  measured  in 
the  same  apparatus  and  under  identical  conditions  very  different 
values  are  obtained.  These  differences  have  been  shown  to  be  due 
in  part  to  variations  in  the  speed  with  which  the  different  ions 
travel  when  attracted  by  a  charge  of  the  same  intensity,  and  in 
part  to  the  fact  that  the  different  electrolytes  are  not  dissociated 
to  the  same  extent. 

When  the  conductivities  of  solutions  containing  different  con- 
centrations of  the  same  electrolyte  are  measured  under  identical 
conditions,  and  the  results  are  divided  by  the  respective  concentra- 
tions it  is  found  that  the  quotients  obtained  for  the  weaker  solu- 
tions exceed  those  obtained  for  the  stronger  solutions.  This  seems 


PROPERTIES  OF  SOLUTIONS  39 

to  mean  that  the  percentage  of  electrolyte  which  exists  in  the 
dissociated  condition  is  greater  in  dilute  than  in  concentrated 
solutions.  It  has  been  shown,  however,  that  altho  the  conductivi- 
ties of  all  electrolytes  increase  as  the  concentration  of  the  solution 
decreases,  the  conductivity  attains  a  definite  limiting  value  at  a 
certain  concentration  which  is  not  changed  by  further  dilution. 
It  seems  probable  that  this  limit,  corresponding  to  the  so-called 
" maximum  conductivity/'  represents  the  conductivity  of  the 
completely  dissociated  electrolyte.  If  this  conclusion  is  accepted 
the  ratio  between  the  conductivity  of  a  solution  of  any  electrolyte 
and  the  maximum  conductivity  of  that  electrolyte  is  a  measure  of 
the  " degree  of  dissociation"  of  the  electrolyte  in  the  solution 
concerned. 

Extent  to  Which  Different  Electrolytes  are  Dissociated. 
Some  of  the  results,  showing  the  extent  to  which  solutions  contain- 
ing different  concentrations  of  a  number  of  electrolytes  are  dis- 
sociated, which  were  obtained  by  the  method  just  outlined,  are 
given  in  the  accompanying  table.*  The  first  column  gives  the 
concentrations  in  moles  per  liter,  the  remaining  columns  the  per- 
centage of  dissociation  of  the  given  reagents  at  different  con- 
centrations. It  is  now  known  that  the  method  here  used 
gives  results  which  are  only  rough  approximations  of  the  correct 
values  for  solutions  whose  concentrations  exceed  molar,  prob- 
ably owing  to  the  resistance  offered  by  large  concentrations  of 
non-ionized  molecules. 

The  differences  between  the  percentages  given  for  strong  acids 
like  nitric,  hydrochloric,  and  sulfuric  and  a  weak  acid  like  acetic  are 
striking,  even  where  the  concentrations  are  below  molar.  Simi- 
lar differences  are  shown  between  the  figures  for  a  strong  base  like 
potassium  hydroxide,  and  a  weak  base  like  ammonium  hydroxide. 
They  are  found  to  be  characteristic  of  all  acids  and  bases  and 
there  is  abundant  evidence  for  the  statement  that  what  is  com- 
monly known  as  the  " strength"  of  an  acid  or  base  depends  upon 
the  extent  to  which  it  is  dissociated  at  different  concentrations. 

*  From  data  of  Kohlrausch  and  Holborn,  Leitvermogen  der  Electrolyte,  160. 


40 


QUANTITATIVE  CHEMICAL  ANALYSIS 


Cone. 

HCl 

HN03 

H2S04 

H(C2H302) 

NaCl 

KOH 

(NH4)OH 

10 

17.08 

17.44 

19.02 

0.05 

19.14 

0.08 

7 

28.17 

28.53 

28.67 

0.14 

33  00 

0  17 

5 

40.37 

40.16 

36.68 

0.27 

38.92 

45.21 

0.31 

4 

48.14 

49.60 

41.14 

0.36 

44.84 

52.22 

0.40 

3 

57.03 

58.66 

45.32 

0.50 

51.50 

60.08 

0.55 

2 

67.37 

68.80 

49.73 

0.75 

59.07 

68.72 

0.80 

1 

79.84 

82.66 

,53.00 

1.23 

67.82 

78.63 

1.35 

0.5 

86.74 

86.40 

55.71 

1.87 

73.74 

84.19 

2.06 

0.1 

93.10 

93.33 

61.14 

4.30 

84.32 

91.02 

5 

The  table  shows  further,  that  sodium  chloride  resembles  the 
strong  acids  and  bases  rather  than  weak  ones,  and  a  large  amount 
of  experimental  work  is  available  which  shows  that  most  salts, 
with  the  exception  of  mercuric  cyanide  and  certain  other  salts  of 
mercury  and  cadmium,  are  largely  dissociated. 

It  has  also  been  shown  that  water  possesses  the  property  of 
causing  solutes  to  dissociate  to  a  greater  extent  than  any  other 
solvent;  alcohol  possesses  this  property  to  some  extent,  but  the  re- 
maining organic  solvents  yield  solutions  which  are  non-conductors. 

Importance  of  the  Electrolytic  Dissociation  Theory.  This 
theory  is  of  especial  importance  in  the  study  of  quantitative 
analysis  owing  to  the  fact  that  many  of  the  chemical  reactions 
upon  which  quantitative  processes  are  based  are  reactions  between 
electrolytes,  and  there  are  decided  differences  between  reactions  of 
this  type  and  those  in  which  electrolytic  dissociation  plays  no  part. 
In  general,  the  ions  possess  a  much  greater  chemical  activity  than 
undissociated  molecules,  and  the  extent  to  which  two  reagents 
react  with  each  other,  and  the  speed  with  which  they  react  is  often 
largely  determined  by  the  extent  to  which  these  reagents  or  the 
products  which  result  from  their  interaction  are  dissociated. 

The  theory  enables  us  to  understand  a  large  number  of  facts 
which  are  difficult  to  explain  on  any  other  basis,  and  to  predict 
with  a  fair  degree  of  certainty  many  effects  which  can  be  used  to 
advantage  in  analytical  chemistry. 


CHAPTER  V 

THE   FACTORS   WHICH   DETERMINE   CHEMICAL  EQUILIBRIUM 

Equilibrium  and  Reaction  Velocity.  When  two  substances 
react  chemically  they  are  in  a  condition  of  unstable  equilibrium 
with  respect  to  each  other;  when  no  further  changes  in  the  relative 
masses  of  these  substances  are  taking  place,  " equilibrium"  has 
been  reached.  This  condition  is  also  defined  by  the  statement 
that  the  " reaction  velocity"  is  zero,  where  the  term  reaction 
velocity  is  defined  as  the  mass  of  one  or  both  of  the  original  sub- 
stances transformed  into  new  substances  during  some  unit  of  time. 
The  velocity  of  many  chemical  reactions,  especially  those  desig- 
nated as  " explosive"  must  be  expressed  by  very  large  numbers, 
even  when  the  unit  of  time  adopted  is  the  second;  that  of  other 
reactions  is  so  small  that  the  day  is  the  more  convenient  unit  to 
employ.  Most  of  the  reactions  which  are  of  importance  in  quan- 
titative analysis  have  velocities  which  are  too  great  to  be  deter- 
mined with  even  approximate  accuracy. 

Homogeneous  and  Heterogeneous  Equilibrium.  In  discuss- 
ing the  subject  of  chemical  equilibrium  and  reaction  velocity  a  very 
important  factor  to  be  considered  is  whether  all  the  reacting 
substances,  and  all  of  the  products  of  the  reaction,  exist  in  the  same 
phase  and  the  nature  of  this  phase.  If  all  the  substances  con- 
cerned are  gases,  or  if  all  remain  dissolved  in  the  same  liquid  phase 
thruout  the  reaction  period,  their  respective  concentrations  remain 
uniformly  distributed  thruout  the  entire  mass,  and  the  resulting 
equilibrium  is  called  "  homogeneous."  If  the  reacting  substances 
exist  as  two  distinct  phases,  or  if  two  distinct  phases  result  as  the 
reaction  progresses,  the  resulting  equilibrium  is  called  "  hetero- 

41 


42  QUANTITATIVE  CHEMICAL  ANALYSIS 

geneous."  In  homogeneous  equilibrium  the  reaction  velocity  is 
uniform  at  all  points  thruout  the  reacting  mass;  in  heterogeneous 
equilibrium  the  reaction  velocity  may  differ  in  the  different  phases, 
and  may  be  reduced  to  practically  zero  except  at  the  surfaces  of 
contact  between  the  different  phases. 

A  condition  of  perfect  equilibrium  between  the  different  phases 
of  a  heterogeneous  system  must  result  if  they  are  allowed  to  remain 
in  contact  for  a  sufficient  length  of  time,  but  the  extent  of  the 
surfaces  cf  contact  between  these  phases  and  the  rates  at  which 
the  products  of  the  reaction  diffuse  away  from  the  immediate 
neighborhood  of  these  surfaces  materially  affect  the  time  needed 
for  the  establishment  of  this  equilibrium. 

Factors  Affecting  Chemical  Equilibrium.  There  are  four  fac- 
tors which  materially  affect  the  direction  and  rate  of  progress  of 
chemical  reactions:  first,  the  chemical  properties  of  the  reacting 
substances;  second,  the  concentrations  of  the  substances  taking 
part  in  the  reaction;  third,  the  temperature;  and  fourth,  the 
pressure. 

As  regards  the  first  of  these  factors  our  present  knowledge 
suggests  the  theory  that  among  the  other  specific  properties  with 
which  every  substance  is  endowed  is  a  certain  intensity  of  chemical 
energy  or  chemical  potential,  and  in  general,  any  two  substances 
tend  to  react  with  each  other  to  an  extent  directly  dependent  upon 
the  difference  between  the  intensity  of  the  chemical  energy  asso- 
ciated with  them.  In  other  words,  there  is  a  universal  tendency 
for  the  equalization  of  chemical  intensities  just  as  there  is  a  uni- 
versal tendency  for  the  equalization  of  heat  intensities,  and  no 
reaction  takes  place  which  does  not  involve  a  reduction  in  the 
chemical  potential  of  the  mixture. 

The  action  of  the  second  factor  is  expressed  in  the  "Law  of 
Mass  Action/'  which  states  that  the  speed  of  the  reaction  between 
any  two  substances  in  a  mixture  is  proportional  to  the  product  of 
the  concentrations  of  these  substances  in  that  mixture,  where  the 
concentrations  are  expressed  in  moles  per  unit  volume.  According 


FACTORS  WHICH  DETERMINE  CHEMICAL  EQUILIBRIUM      43 

to  this  law  the  expression  for  a  reaction  between  the  substances 
A  and  B  which  unite  to  form  the  substances  P  and  Q  is 


In  this  expression  (C^),  etc.,  represent  the  concentrations  of  these 
molecules,  a,  6,  etc.,  the  number  of  moles  of  these  substances 
concerned  in  the  reaction,  k  a  constant  representing  the  speed  of 
the  reaction  between  A  and  B,  and  kf  a  constant  representing  the 
speed  of  the  reaction  between  P  and  Q.  Since  k  and  kf  are  both 
constants  the  expression  can  be  simplified  by  dividing  by  k'  and 
substituting  K  for  k  -r-  k']  it  then  becomes 


It  might  have  been  simplified  by  dividing  by  k,  in  which  case 
k'  -?-  k  OY  K  would  have  a  value  represented  by  the  reciprocal  of 
that  given  in  the  above  expression.  Thruout  this  book  the  former 
method  will  be  employed,  that  is,  where  K  is  referred  to,  it  should 
be  understood  to  represent  the  constant  obtained  when  K  appears 
on  the  left  of  the  sign  of  equality  in  the  mass  law  expression. 

It  is  evident  that  K  represents  a  ratio,  whose  value  depends  on 
the  specific  properties  of  the  four  substances  A,  B,  P  and  Q,  and 
not  upon  the  concentration  in  which  any  one  or  two  of  them  exist 
in  the  mixture.  If  a  mixture  is  made  in  which  (CP)P  •  (CQ)q  -f- 
(C^)a  •  (CB)b  exceeds  K,  (CA)  and  (CB)  must  increase,  and  (CP)  and 
(Co)  must  decrease  until  the  mass  law  expression  is  satisfied, 
that  is,  the  reaction  must  progress  from  right  to  left.  If  this 
quotient  is  less  than  K  the  reaction  must  progress  from  left  to 
right.  In  general,  if  the  value  of  K  is  large  the  predominating 
tendency  is  for  the  reaction  to  proceed  from  left  to  right;  if  it  is 
a  small  fraction  of  unity  the  predominating  tendency  is  for  it  to 
progress  from  right  to  left.  Since  the  value  of  K  determines  to  a 
large  extent  the  direction  in  which  reactions  progress  it  is  called 
the  "  reaction  constant"  or  "equilibrium  constant." 


44  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  effect  of  temperature  upon  a  reaction  depends  upon  whether 
it  absorbs  or  liberates  heat.  Increasing  the  temperature  displaces 
the  equilibrium  in  the  direction  of  that  reaction  which  absorbs 
heat,  that  is,  it  increases  K  if  heat  is  absorbed  when  the  reaction 
progresses  from  left  to  right;  it  displaces  equilibrium  in  the 
reverse  direction  if  heat  is  given  out,  that  is,  it  decreases  K  if  heat 
is  liberated  when  the  reaction  progresses  from  left  to  right. 

The  effect  of  pressure  upon  a  reaction  depends  upon  whether 
the  volume  of  the  reacting  mass  is  increased  or  decreased  as  the 
reaction  progresses.  If  it  is  increased,  increasing  the  pressure 
favors  the  reaction,  and  increases  the  value  of  K;  if  it  is  decreased 
it  inhibits  the  reaction  and  decreases  the  value  of  K.  The  volume 
changes  in  reactions  in  which  only  solid  and  liquid  phases  are 
concerned  are  so  small  that  they  have  an  inappreciable  effect  upon 
the  value  of  K.  When  gases  are  produced  or  absorbed  as  the 
reaction  progresses  pressure  has  a  large  effect  upon  the  value  of  K. 

An  Illustration  of  Homogeneous  Equilibrium.  The  manner 
in  which  the  factors  named  in  the  preceding  section  affect  a  simple 
reaction  involving  homogeneous  equilibrium  can  be  most  easily 
comprehended  by  considering  a  specific  case,  such  as  the  action 
between  acetic  acid  and  ethyl  alcohol.  These  substances  as  well 
as  the  products  of  their  interaction  are  soluble  in  each  other  to  an 
unlimited  extent.  When  acetic  acid  is  added  to  alcohol  the  result- 
ing reaction  is  represented  by 

(C2H5)HO  +  (CH3)COOH->  (C2H5)COO(CH3)  +  H20. 

If  water  is  added  to  ethyl  acetate,  alcohol  and  acetic  acid  are 
produced,  that  is,  the  reaction  progresses  in  the  reverse  direction 
when  the  concentrations  of  water  and  ethyl  acetate  are  large.  If 
either  of  the  two  mixtures  are  allowed  to  stand  until  equilibrium 
has  been  attained  the  concentrations  of  the  four  substances  in  the 
mixture  must  be  in  accord  with  the  expression 

K=     (C4H802)  •  (HaO) 
"  (C2H402)  •  (C2H60) ' 


FACTORS  WHICH  DETERMINE   CHEMICAL  EQUILIBRIUM      45 

in  which,  and  in  all  of  the  subsequent  pages  of  this  book,  a  chemical 
formula  enclosed  in  brackets  designates  concentrations  of  the 
corresponding  substance  expressed  in  moles  per  liter.  The  value 
of  K  in  this  expression  has  been  found  to  be  4  and  it  is  easy  to 
calculate  the  composition  of  the  mixture  which  results  when  known 
quantities  of  alcohol  and  acetic  acid  or  of  ethyl  acetate  and  water 
are  mixed.  Suppose  we  make  a  mixture  of  240  gm.  of  acetic  acid, 
138  of  alcohol  and  54  of  water.  If  we  represent  the  volume  of  the 
mixture  before  any  action  takes  place  by  V  then  (C^EUC^)  in  that 
mixture  is  240  -f-  60  V  or  4  -r-  7,  (C2H60)  is  138  -f-  46  V  or  3  -5-  V 
and  (H20)  is  54  ^  18  V  or  3  -f-  V. 

If  x  represents  the  moles  of  ethyl  acetate  present  after  equilib- 
rium has  been  attained,  x  also  represents  the  moles  of  water  pro- 
duced by  the  reaction,  also  (4  —  x)  the  moles  of  acetic  acid  and 
(3  —  x)  the  moles  of  alcohol  left  uncombined.  If  we  represent 
the  final  volume  of  the  mixture  by  Vf  the  mass  law  expression 
becomes 

4  —  x    3  —  x      _  x_    3  +  x 
y         y          ~  y  "     y    ' 

from  which  48  -  28  x  +  4  x2  =  3  x  +  x*. 

When  solved  for  x  the  latter  is  found  to  have  the  value  1.9  which 
means  that  the  final  mixture  contains  1.9  X  88  or  167.2  gm.  of 
ethyl  acetate  and  54  +  (1.9  X  18)  or  57.4  gm.  of  water. 

Since  the  formation  of  ethyl  acetate  and  water  liberates  heat, 
increasing  the  temperature  decreases  the  value  of  K  and  decreases 
the  amount  of  ethyl  acetate  and  water  produced. 

Since  no  gases  are  either  produced  or  absorbed,  pressure  has  no 
appreciable  effect  upon  the  value  of  K  and  does  not  affect  the 
amount  of  ethyl  acetate  and  water  formed. 

Reversible  and  Irreversible  Reactions.  In  the  reaction  dis- 
cussed in  the  previous  section  the  constant  K  has  a  moderately 
large  value;  this  means  that  altho  the  tendency  for  the  reaction 
to  progress  in  one  direction  preponderates  over  its  tendency  to 


46  QUANTITATIVE  CHEMICAL   ANALYSIS 

progress  in  the  reverse  direction,  both  tendencies  are  recognizable, 
and  where  equivalent  concentrations  of  the  reacting  substances 
are  used,  large  concentrations  of  all  four  substances  are  present  in 
the  resulting  mixture.  Such  reactions  are  spoken  of  as  "  rever- 
sible/7 

In  many  reactions,  however,  the  value  of  the  constant  K  is 
either  very  large  or  small;  this  means  that  the  tendency  for  the 
reaction  to  progress  in  one  direction  greatly  preponderates  over 
the  reverse  tendency,  and  with  equivalent  concentrations  of  the 
reacting  constituents,  conversion  into  the  resulting  products  is 
practically  complete.  Such  reactions  are  spoken  of  as  "  irre- 
versible/7 altho  strictly  speaking,  all  reactions  are  to  be  regarded 
as  reversible  to  some  degree  even  though  it  may  be  difficult  to 
recognize  the  fact  experimentally.  Most  quantitative  processes 
which  depend  upon  the  employment  of  chemical  reactions  are 
inaccurate  unless  the  substance  under  treatment  is  almost  com- 
pletely transformed  into  the  desired  compound,  and  reactions 
whose  constants  are  large  are  the  only  ones  which  can  be  em- 
ployed to  advantage  in  such  processes.  The  factors  already  dis- 
cussed may  be  used  to  assist  in  displacing  the  equilibrium  of 
reversible  reactions  in  the  desired  direction. 

Reactions  Involving  Heterogeneous  Equilibrium.  The  factors 
which  affect  chemical  reactions  also  affect  the  processes  of  evapora- 
tion and  solution,  and  the  simplest  illustrations  of  heterogeneous 
equilibrium  are  those  in  which  two  phases  containing  different 
concentrations  of  the  same  substance  are  in  equilibrium  with  each 
other.  This  is  true  of  a  solid  or  liquid  which  is  in  equilibrium  with 
its  vapor,  or  of  a  solid  which  is  in  equilibrium  with  a  solution.  All 
such  systems  conform  to  a  very  simple  law,  namely,  that  the  ratio 
between  the  concentrations  of  the  substance  concerned  in  the  two 
phases  is  constant  for  any  given  temperature.  When,  for  example, 
a  solid  substance  is  brought  into  contact  with  a  liquid  it  continues 
to  dissolve  until  the  solution  is  saturated,  that  is,  when  equilibrium 
between  the  two  phases  has  been  attained  the  solution  contains 


FACTORS  WHICH   DETERMINE   CHEMICAL  EQUILIBRIUM      47 

a  fixed  concentration  of  the  dissolved  substance,  and  since  the 
solid  phase  represents  the  pure  substance  its  concentration  does 
not  vary,  but  depends  upon  its  specific  gravity.  Hence  the 
general  expression  for  the  equilibrium  condition  becomes 

K  =  Cj 

in  which  C  represents  the  concentration  of  the  saturated  solution. 
The  more  complex  examples  of  heterogeneous  equilibrium  will  be 
discussed  in  Chapters  X,  XVI  and  XXXII. 

Reaction  Velocity  and  Catalysis.  The  speed  with  which  a 
reaction  progresses  depends  upon  the  specific  properties  of  the 
reacting  substances  and  their  concentrations;  in  general,  it  is  more 
than  doubled  for  every  increase  of  10°  in  the  temperature  of  the 
reacting  mass. 

The  reaction  velocity  of  certian  processes  is  increased  in  an 
abnormal  manner  by  certain  substances  and  decreased  by  others. 
The  former  class  of  substances  are  known  as  positive  —  and  the 
latter  as  negative  —  catalyzers.  Very  small  concentrations  of  a 
catalyzer  may  produce  very  marked  effects,  and  as  they  do  not 
suffer  an  appreciable  change  in  concentration  they  must  act 
indirectly,  that  is,  form  one  or  more  intermediate  compounds  with 
the  reacting  substances  which  at  once  decompose  into  the  original 
catalyzer  and  the  desired  end  product.  According  to  this  theory 
the  velocity  of  the  reaction  is  increased  because  the  velocities  of 
the  intermediate  reactions  greatly  exceed  that  of  the  direct  reaction 
between  the  original  substances.  They  have  no  effect  upon  the 
value  of  the  equilibrium  constant,  but  increase  the  speed  at  which 
a  condition  of  equilibrium  is  attained. 


CHAPTER  VI 

THE  CHEMICAL  ACTIVITY  OF  ELECTROLYTES 

Preliminary  Statements.  In  outlining  the  general  principles 
which  determine  reaction  velocity  and  equilibrium  in  the  previous 
chapter  the  possibility  of  electrolytic  dissociation  was  not  consid- 
ered. The  principles  there  set  forth  are  universally  valid,  and  if 
the  dissociation  theory  is  also  accepted  it  becomes  necessary  to 
point  out  how  these  principles  should  be  applied  to  the  study  of 
reactions  between  electrolytes.  Since,  according  to  this  theory, 
the  ions  possess  a  greater  chemical  activity  than  the  original 
molecules,  the  concentrations  of  the  ions  should  determine  the 
reaction  velocity  and  the  resulting  equilibrium,  to  a  greater  extent 
than  the  concentration  of  the  original  molecules.  Experience 
confirms  this  suggestion,  for  a  great  variety  of  well-established 
facts  show  that  the  chemical  properties  of  solutions  of  largely 
dissociated  electrolytes  can  be  most  easily  understood  by  assuming 
that  these  properties  depend  upon  the  concentrations  of  the  ions 
which  they  contain. 

The  Law  of  Electro-neutrality.  Whenever  a  compound  un- 
dergoes electrolytic  dissociation  the  quantity  of  positive  electricity, 
which  is  associated  with  the  resulting  cations,  exactly  equals  the 
quantity  of  negative  electricity,  which  is  associated  with  the 
resulting  anions,  and  the  solution  obtained  is,  therefore,  electri- 
cally neutral.  The  quantity  of  positive  charge  which  is  associated 
with  the  hydrogen  ion  is  fixed  and  invariable;  all  other  cations 
bear  positive  charges,  which  are  either  equal  to,  or  simple  multiples 
of,  this  charge;  all  anions  bear  negative  charges  which  are  either 
equivalent  to  the  positive  charge  associated  with  the  hydrogen  ion, 

48 


THE   CHEMICAL  ACTIVITY  OF  ELECTROLYTES  49 

or  to  simple  multiples  of  it.  The  value  of  these  multiples  is 
determined  in  all  cases  by  the  valence  of  the  element,  or  the  com- 
bination of  elements  representing  the  composition  of  the  ion,  in 
the  undissociated  molecule.  Those  elements  which  form  com- 
pounds representing  different  degrees  of  oxidation  also  form  ions 
associated  with  different  amounts  of  electrical  charge,  and  the 
properties  of  such  ions  depend  upon  the  charges  with  which  they 
are  associated.  Thus  the  cation  which  results  from  the  dissocia- 
tion of  a  ferrous  salt  differs  from  the  cation  resulting  from  the 
dissociation  of  a  ferric  salt,  in  that  the  former  consists  of  an  ion, 
atom  associated  with  two  positive  charges,  the  latter  of  an  atom 
associated  with  three  positive  charges. 

When  solutions  containing  different  electrolytes  are  brought 
together  various  changes  may  take  place.  Certain  ions  which 
possess  but  slight  affinity  for  their  charges  may  give  them  up  to 
other  elements  or  groups  of  elements  and  form  more  stable  ions. 
Certain  di-  or  tri-valent  ions  may  lose  a  half  or  a  third  of  their 
charges,  or  certain  uni-  or  di-valent  ions  may  take  up  charges  and 
become  di-  or  tri-valent.  In  other  instances  certain  charges  may 
disappear  entirely  from  the  solution.  The  law  of  electro-neutrality 
requires  that,  whatever  the  character  or  complexity  of  these 
changes,  the  solutions  must  remain  electrically  neutral;  that  is, 
wherever-  positive  'charges  disappear,  an  equivalent  number  of 
negative  charges  must  disappear  simultaneously;  and  wherever 
positive  charges  are  added  to  the  solution,  equivalent  amounts  of 
negative  charges  must  be  added  to  it  at  the  same  time. 

The  Chemical  Activity  of  Acids.  All  acids  which  dissociate 
to  an  appreciable  extent,  produce  corresponding  concentrations 
of  hydrogen  ions,  and  the  characteristic  properties  of  aqueous 
solutions  of  this  class  of  substances  are  dependent  upon  this  fact. 
In  so  far  as  these  general  properties  are  concerned,  the  element  or 
combination  of  elements  with  which  the  hydrogen  is  combined 
in  the  undissociated  molecule  is  of  importance  mainly  in  that  it 
determines  the  extent  to  which  the  acid  undergoes  dissociation 


50  QUANTITATIVE  CHEMICAL  ANALYSIS 

when  dissolved  in  water.  Thus  the  chlorine  atom  possesses  a 
greater  affinity  for  a  negative  charge  than  the  C2H302  group,  hence 
the  sum  of  the  forces  which  tend  to  bring  about  dissociation  of  the 
hydrochloric  acid  molecule  will  exceed  the  sum  of  the  forces  which 
tend  to  bring  about  dissociation  of  the  acetic  acid  molecule;  since 
solutions  of  both  acids  must  remain  electrically  neutral,  the  con- 
centration of  the  hydrogen  ions  in  a  solution  of  hydrochloric  acid 
must  exceed  the  concentration  of  the  hydrogen  ions  in  solutions 
of  acetic  acid  of  equivalent  concentration. 

The  chemical  activity  of  an  acid  can  be  measured  by  determining 
the  rate  at  which  solutions  containing  known  concentrations  of 
the  acid  in  question  affect  certain  chemical  transformations.  The 
chemical  activities  of  solutions  containing  equivalent  amounts  of 
some  of  the  more  important  acids  have  been  determined  by  a 
variety  of  methods,  and  the  differences  in  the  values  thus  obtained 
are  found  to  agree  at  least  approximately  with  the  corresponding 
variations  in  the  concentrations  of  the  hydrogen  ion  present,  as 
calculated  by  the  method  described  on  page  39.  The  conduc- 
tivity of  an  aqueous  solution  of  an  acid  containing  one  equivalent 
in  grams  per  liter  is,  therefore,  a  measure  of  its  "strength."  The 
comparative  conductivities  of  some  of  the  more  important  acids 
are  given  in  the  following  table  in  which  the  conductivity  of 
hydrochloric  acid  has  been  arbitrarily  given  the  value  of»  100. 

Hydrochloric  acid 100 

Hydrobromic  acid 104 

Nitric  acid 99.6 

Sulfuric  acid. 66.4 

Oxalic  acid 19.7 

Phosphoric  acid 

Arsenic  acid 5 . 38 

Formic  acid 1 . 68 

Acetic  acid 0 . 42 

Succinic  acid 0 . 58 

Tri-chlor  acetic  acid '. 62 . 3 

These  numbers  relate  to  normal  concentrations  only,  and  increas- 
ing or  decreasing  the  concentration  does  not  increase  or  decrease 
the  conductivity,  and,  therefore,  the  strength  of  the  solution  to 


THE  CHEMICAL  ACTIVITY  OF  ELECTROLYTES  51 

a  corresponding  degree.  The  concentration  of  the  hydrogen  ion 
present  in  any  solution  of  an  acid  equals  the  product  of  the  numbers 
representing  the  concentration  of  the  acid,  in  gram  equivalents 
per  liter,  and  the  degree  of  dissociation  of  the  acid  at  that  concen- 
tration. Since  the  degree  of  dissociation  increases  with  the  dilu- 
tion the  series  of  numbers  given  in  the  table  should  become  more 
nearly  equal  with  decreasing  concentration.  The  highest  attain- 
able concentration  of  hydrogen  ion  is  found  in  a  solution  of  nitric 
acid  having  a  specific  gravity  of  1.19;  this  solution  contains  about 
31  per  cent  of  HN03,  of  which  about  35  per  cent  is  dissociated, 
hence  the  concentration  of  hydrogen  ion  represented  by  such  a 
solution  is  about  2  gm.  per  liter. 

The  non-acidic  properties  of  solutions  of  acids  are  determined 
by  the  concentrations  of  the  anions  present,  and  also,  especially 
with  those  acids  which  are  but  slightly  dissociated,  upon  the  un- 
dissociated  molecules,  whose  chemical  activity  cannot  be  entirely 
disregarded. 

The  Chemical  Activity  of  Bases.  All  bases  which  dissociate 
to  an  appreciable  extent  produce  corresponding  concentrations  of 
the  hydroxyl  (HO)  ion,  and  this  fact  determines  the  characteristic 
properties  of  aqueous  solutions  of  this  class  of  substances.  The 
extent  to  which  different  bases  dissociate,  depends  upon  the  nature 
of  the  cation  to  which  they  give  rise,  or  more  specifically  upon  the 
strength  of  the  affinity  of  the  cation  for  its  positive  charge.  The 
chemical  activities  of  solutions  containing  equivalent  concentra- 
tions of  different  bases  have  been  determined  by  methods  similar 
to  those  used  in  the  study  of  acids.  The  results  show  a  substantial 
agreement  between  the  chemical  activity  and  the  degree  of  dis- 
sociation, that  is  the  " strength"  of  a  base  as  determined  by  the 
concentration  of  the  hydroxyl  ion  which  result  when  it  is  dissolved 
in  water.  The  comparative  conductivities  of  fortieth  normal 
solutions  of  some  of  the  more  common  bases  are  represented  by 
the  numbers  of  the  following  table,  in  which  the  number  100  has 
been  arbitrarily  assigned  to  potassium  hydroxide. 


52  QUANTITATIVE  CHEMICAL  ANALYSIS 

Potassium  hydroxide. 100 

Sodium  hydroxide 92 

Lithium  hydroxide 88 . 2 

Ethyl  amine 12.46 

Ammonium  hydroxide 2 . 53 

The  Chemical  Activity  of  Salts.  The  salts  of  most  acids  and 
bases  are  largely  dissociated  in  aqueous  solutions  of  moderate 
concentration,  hence  the  concentrations  of  the  anions  or  cations 
present  in  solutions  containing  equivalent  concentrations  of  salts 
of  the  same  acid  or  base  are  more  nearly  equal,  and  the  chemical 
properties  of  such  solutions  are  more  nearly  uniform.  Certain 
salts,  especially  certain  salts  of  mercury  and  cadmium  are  peculiar 
in  that  they  ionize  to  a  slight  extent  only,  and  as  a  consequence 
the  reactions  of  these  salts  are  somewhat  anomalous.  The  phe- 
nomenon of  "hydrolysis,"  which  will  be  discussed  in  a  succeeding 
section,  is  the  cause  of  marked  peculiarities  in  the  chemical  prop- 
erties of  certain  salts. 

Dissociation  in  Solutions  Containing  a  Single  Electrolyte. 
The  dissociation  of  an  electrolyte  should  obey  the  law  of  mass 
action.  The  general  expression  representing  the  dissociation  of 
a  molecule  AB,  which  yields  two  ions  A+  and  B~  is: 

(A+)  •  (B-) 


or    k  = 


(AB) 


The  value  of  k  in  this  expression  depends  upon  the  specific  proper- 
ties of  the  electrolyte  and  the  temperature;  it  expresses  the 
tendency  of  the  electrolyte  to  undergo  dissociation,  and  is  generally 
known  as  the  "dissociation  constant." 

It  was  noted  in  Chapter  IV  that  the  degree  of  dissociation  of 
an  electrolyte  increases  with  the  dilution,  and  an  expression  which 
represents  the  effect  of  dilution  on  dissociation  can  be  derived  from 
the  mass  law.  If  we  represent  the  quantity  of  electrolyte  present, 
when  expressed  in  moles,  by  a  and  the  fraction  of  it  which  is  dis- 
sociated by  x,  ax  must  represent  the  concentration  of  both  anion 
and  cation  and  (a  —  ax)  that  of  the  undissociated  electrolyte.  If 


THE   CHEMICAL  ACTIVITY  OF  ELECTROLYTES  53 

the  volume  of  solution  be  represented  by  V  the  mass  law  expression 
is 

a  —  ax   ,  ]_  (ax)     (ax)  ,  a(x)2 

~~r     i  (FT; -or         =  (i  -  xw' 

This  formula,  which  was  first  proposed  by  Ostwald,  has  been 
tested  by  determining  the  effect  of  dilution  on  the  conductivity 
of  a  long  series  of  electrolytes.  When  the  value  of  "k  was  calculated 
from  these  determinations  it  was  found  to  be  nearly  constant  for 
all  the  weaker  acids  and  bases,  but  was  found  to  decrease  decidedly 
with  dilution  for  the  strong  acid  and  bases,  and  for  most  salts. 
This  means  that  the  dissociation  of  those  electrolytes  which  are 
largely  dissociated  does  not  increase  with  the  dilution  as  much  as 
the  law  of  mass  action  demands.  Several  modifications  of  the 
expression  designed  to  more  accurately  represent  the  effect  of 
dilution  on  the  dissociation  of  these  electrolytes  have  been  sug- 
gested; they  all  contain  one  or  more  empirically  determined 
constants  and  need  not  be  considered  here. 

The  use  of  the  expression  given  can  be  shown  by  a  simple  illus- 
tration. Let  us  suppose  that  we  have  two  liters  of  a  solution  which 
contains  20  gm.  of  acetic  acid  and  let  us  represent  the  fraction 
dissociated  by  x.  Then  the  number  of  moles  present  if  there  were 
no  dissociation  would  be  20  -f-  60,  or  0.333,  and  both  (H+)  and 
(C2H302~)  are  represented  by  0.333  x,  while  (C2H402)  is  repre- 
sented by  (0.333  —  0.333 x).  The  dissociation  constant  of  acetic 
acid  has  the  value  1.8  X  10~5;  by  making  the  proper  substitutions 
in  the  general  equation  we  get 
(0.333  xY 


(0.333-  0.333  x)2 
or 

0.333  x*  +  3.6  X  10-5z  =  3.6  X  10~5, 

from  which  we  obtain          x  =  0.0108. 

Hence  the  degree  of  dissociation  and  the  concentration  of  the  i 


in  any  solution  -of.  such  electrolytes  can  be  calculated  if  the  con- 
centration^ and  dissociation  constant  are  known.     It  might  be 


54  QUANTITATIVE   CHEMICAL   ANALYSIS 

noted  that  when  the  total  concentration  of  the  electrolyte  is  1, 
and  k  has  a  small  value  the  value  of  x  is  approximately  equal  to  the 
square  root  of  k.  For  instance,  the  concentration  of  H+  in  a 
normal  solution  of  acetic  acid  is 

1  X  (1.8  X  10-5)',     or    0.00425. 

Dissociations.  in  Solutions  Containing  Two  Electrolytes  Which 
Yield  a  Common  Ion.  It  can  be  shown  that  when  two  solutions 
which  contain  equal  concentrations  of  the  same  ion  are  mixed  in 
any  proportions  whatever,  the  dissociation  of  the  two  electrolytes 
in  the  resulting  mixture  satisfies  the  law  of  mass  action  if  the  con- 
centration of  the  common  ion  remains  unchanged.  Such  solutions 
are  designated  as  "isohydric."  Solutions  of  the  two  electrolytes 
are  isohydric  when  the  product  of  the  concentration  of  the  elec- 
trolyte and  its  degree  of  dissociation  at  this  concentration,  is  the 
same  for  both  solutions.  When  both  electrolytes  are  but  slightly- 
dissociated  solutions  of  them  are  approximately  isohydric  when 
their  concentrations  are  inversely  proportional  to  their  dissocia- 
tion constants. 

When  solutions  which  are  not  isohydric  are  mixed,  changes  in  the 
dissociation  of  both  electrolytes  are  inevitable.  In  such  mixtures 
the  concentration  of  the  common  ion  represents  the  sum  of  the 
concentrations  due  to  the  dissociation  of  both  electrolytes.  If  C 
represents  the  total  concentration  of  one  electrolyte  and  C'  that  of 
the  other,  and  X  and  Y  their  respective  degrees  of  dissociation, 
the  concentration  of  the  common  ion  is  (CX  +  C'Y)  and  assuming 
that  they  are  both  weak  electrolytes  the  following  expressions  are 
true. 


,  _        (CX  +  CiF)  _      X     frv      r  v. 
-  ^(( 


-,,  _  CiY  (CX  +  CiY)  _      Y     ,rv  \  ri 

Ci(i-y)      ~T=Y(CX 

If  we  divide  (3)  by  (4)  we  obtain 

X          Y  , 


THE  CHEMICAL  ACTIVITY  OF  ELECTROLYTES  55 

that  is,  the  ratio  of  the  dissociated  to  the  undissociated  molecules 
of  one  electrolyte  bears  the  same  relation  to  the  corresponding 
ratio  for  the  other,  as  the  dissociation  constants  of  the  respective 
electrolytes  bear  to  each  other. 

If  it  is  assumed  that  the  second  electrolyte  is  added  as  a  solid, 
so  that  the  change  in  volume  is  eliminated,  a  reduction  in  the 
degree  of  dissociation  of  the  first  electrolyte  must  take  place; 
this  change  will  be  large  in  proportion  as  the  dissociation  constant 
of  the  added  electrolyte  is  large  as  compared  with  that  of  the 
original  electrolyte.  The  degree  of  dissociation  of  the  added 
electrolyte  must  be  less  than  it  would  have  been  if  added  to  the 
same  volume  of  water,  and  the  reduction  will  be  large  in  proportion 
as  the  dissociation  constant  of  the  original  electrolyte  exceeds 
that  of  the  added  electrolyte. 

If  the  second  electrolyte  is  added  in  the  form  of  a  solution  the 
effect  of  dilution  on  the  dissociation  of  both  electrolytes  must  also 
be  considered.  The  action  of  either  electrolyte  upon  the  dissocia- 
tion of  the  other  is  large  in  proportion  as  the  composition  of  the 
two  solutions  differ  from  that  of  isohydric  solutions. 

The  "  Repression  of  lonization."  The  most  important  prac- 
tical result  of  the  above  discussion  is  to  give  a  better  under- 
standing of  the  phenomenon  now  known  as  the  "  repression  of 
ionization."  The  chemical  activity  of  certain  reagents  is  greatly 
diminished  by  the  addition  of  certain  electrolytes  which  yield  a 
common  ion.  The  addition  of  potassium  acetate  to  a  solution  of 
acetic  acid  greatly  reduces  the  acidic  properties  of  the  latter;  the 
addition  of  ammonium  chloride  to  a  solution  of  ammonium  hy- 
droxide also  reduces  the  basic  properties  of  this  reagent.  In  both 
cases  the  reagents  added  have  large  dissociation  constants,  and 
those  originally  present  have  small  ones.  If  the  solution  of  potas- 
sium acetate  added  contains  a  greater  concentration  of  C2H302 
ion  than  the  acetic  acid  solution,  the  degree  of  ionization  of  the 
latter  must  be  reduced,  and  the  concentration  of  the  hydrogen 
ion  in  the  resulting  mixture  must  be  less  than  that  of  the  original 


56  QUANTITATIVE  CHEMICAL  ANALYSIS 

solution.  Similarly,  if  the  solution  of  ammonium  chloride  added 
is  sufficiently  concentrated  to  yield  a  greater  concentration  of  NH4 
ion  than  the  ammonium  hydroxide  solution,  the  degree  of  ioniza- 
tion  of  the  latter,  and  hence  the  concentration  of  the  hydroxyl 
ion,  must  be  reduced. 

Reactions  Between  Electrolytes  Which  Do  Not  Yield  a  Com- 
mon Ion.  The  most  important  effects  to  be  considered  here 
result  from  the  formation  of  entirely  new  compounds.  If  both 
electrolytes  yield  one  anion  and  one  cation  at  least  two  undis- 
sociated  molecules,  in  addition  to  the  two  undissociated  molecules 
present  in  the  original  solutions,  should  exist  in  the  resulting 
mixture.  The  concentrations  of  these  molecules  will  depend  for 
the  most  part  upon  their  respective  dissociation  constants.  If 
these  constants  are  large  their  concentrations  will  be  very  small, 
and  the  resulting  mixture  will  retain  for  the  most  part  the  com- 
bined properties  of  the  two  constituent  solutions.  If,  however, 
one  of  these  constants  is  small  this  favors  the  formation  of  the 
new  molecule  at  the  expense  of  the  ions  concerned. 

Reactions  which  Involve  the  Formation  of  Water.  Pure  water 
dissociates  into  hydrogen  and  hydroxyl  ions  to  a  very  slight  extent 
only;  the  value  of  its  dissociation  constant  is  1.2  X  10~14.  When 
an  acid  is  added  to  a  base,  water  and  a  salt  are  formed.  If  both 
acid  and  base  are  strong,  and  the  concentration  of  the  resulting 
mixture  is  small,  their  dissociation  may  be  considered  complete, 
and  with  but  few  exceptions  the  dissociation  of  the  resulting  salt 
can  also  be  considered  complete.  The  essential  feature  of  the 
reaction  therefore  is  the  disappearance  of  hydrogen  and  hydroxyl 
ions  and  the  formation  of  water;  the  concentrations  of  the  anion 
of  the  acid  and  the  cation  of  the  base  remains  practically  constant. 
Hence  the  reaction  is  expressed  by 

H+  +  HO-->H20,     and 


H20 


(H+XHO-) 

Since   H2O  -v-  (H+)  (H0~)   is   the   reciprocal   of   the    expression 
representing  the  dissociation  constant  of  water,  K  has  the  value 


THE  CHEMICAL  ACTIVITY  OF  ELECTROLYTES  57 

1  -f-  1.2  X  10~14   and  therefore   all   reactions  of   this   type    are 
irreversible. 

If  both  acid  and  base  are  but  partly  dissociated  the  reversibility 
of  the  reaction  may  be  large.  The  most  important  equilibrium 
concerned  in  such  reactions  is  expressed  by 

ROH  +  HA-+  H20  +  R+  +  A- 

in  which  ROH  represents  a  weak  base   and  HA  a  weak  acid. 
Three  other  relations  must  also  exist  in  the  final  solution,  namely  : 


_.      (b]  ,    (H+KHO-) 

(ROH)  (HA)  H20 

If  we  multiply  (a)  by  (b)  and  divide  by  (c)  we  obtain  the  expression 


(R+)(A-)(H20)  =  feq- 
(ROH)  (HA) 


This  expression  shows  that  the  value  of  the  constant  for  this  class 
of  reactions  depends  upon,  and  can  be  calculated  from,  the  disso- 
ciation constants  of  the  acid  and  base  and  of  water.  If  the  acid 
is  strong  and  its  dissociation  constant  can  be  represented  with  ap- 
proximate accuracy  by  one,  and  the  general  expression  becomes 

K=—  • 

I^W 

If  the  base  is  strong  its  dissociation  constant  can  be  represented 
with  approximate  accuracy  by  one  and  the  general  expression  be- 
comes 

K  =      • 

KID 

Hydrolysis.     This  represents  the  converse  of  the  class  of  reac- 
tions just  considered.     It  is  expressed  by 

(R+)  +  (A-)  +  H20  ->  (ROH)  +  (HA)  . 


58  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  value  of  K  for  such  reactions  is  evidently  the  reciprocal  of  that 
representing  the  formation  of  a  salt  and  water  from  a  weak  acid 
and  a  weak  base,  namely, 


Evidently  K  has  a  maximum  value  when  ka  and  kb  are  both  very 
small,  but  it  may  be  moderately  large  when  either  of  them  has  a 
value  which  approaches  that  of  kw. 

The  effect  of  hydrolysis  is  most  striking  when  the  salt  yields 
either  a  strong  acid  and  a  very  weak  base,  or  a  strong  base  and  a 
very  weak  acid.  In  the  former  case  the  solution  contains  a  con- 
centration of  hydrogen,  and  in  the  latter  case  of  hydroxyl  ion, 
which  is  directly  proportional  to  the  extent  to  which  the  salt  is 
hydrolyzed,  and  for  this  reason  solutions  of  salts  representing 
combinations  of  strong  acids  and  weak  bases  show  acidic  properties 
and  solutions  of  salts  representing  combinations  of  strong  bases 
and  weak  acids  show  basic  properties.  If  the  dissociation  con- 
stants of  the  acid  and  base  formed  have  the  same  value  the  solution 
will  contain  equivalent  concentrations  of  hydrogen  and  hydoxyl 
ions  and  hence,  such  solutions  are  neutral  even  though  the  salt  is 
hydrolyzed  to  a  much  greater  extent  than  when  one  dissociation 
constant  is  large  and  the  other  small. 

Reactions  Involving  the  Displacement  of  One  Acid  or  Base 
by  Another.  When  a  salt  which  represents  the  result  of  the 
combination  of  a  base  with  a  weak  acid  is  treated  with  a  second 
acid  a  reaction  becomes  possible  which  is  represented  by 

(R+)  (A-)  +  (HA,)  -»  (R+)  +  (Ar)  +  (HA) 

(Ar)(HA) 

X=(A-)(HA2)' 

Two  other  equilibria  must  exist  in  the  resulting  solution,  namely, 


2_,  ,     (b, 

-          --  fcHA2,    anc  -(HAT 


THE   CHEMICAL  ACTIVITY  OF  ELECTROLYTES  59 

If  we  divide  (a)  by  (b)  and  eliminate  (H)  we  obtain 

(Ar)  (HA) 

(A-)  (HA2) 

\ 

Hence  the  reversibility  of  such  reactions  decreases  in  proportion 
as  the  dissociation  constant  of  the  added  acid  exceeds  that  of  the 
acid  from  which  the  original  salt  was  formed.  If  the  dissociation 
constant  of  the  added  acid  can  be  represented  with  approximate 
accuracy  by  one,  the  value  of  K  becomes  the  reciprocal  of  the 
dissociation  constant  of  the  acid  from  which  the  salt  was  formed. 

Similarly  it  can  be  shown  that  the  reaction  constants  of  those 
processes  which  involve  the  displacement  of  one  base  from  a  salt 
by  a  second  base  depend  upon  the  ratio  of  the  dissociation  constant 
of  the  second  base  to  that  of  the  base  from  which  the  original  salt 
was  formed. 

Reactions  Involving  the  Formation  of  Complex  Ions.  Certain 
reactions  depend  upon  the  tendency  which  certain  ions  possess  of 
combining  with  other  ions  or  non-ionized  molecules  to  form  com- 
plex ions.  For  example,  when  a  soluble  silver  salt  is  added  to  a 
soluble  cyanide  a  reaction  takes  place  which  is  represented  by 

Ag+  +  N03~  +  2  K+  +  2  CN-  -»  Ag(CN)2-  +  K+  +  NQr. 

The  essential  feature  of  this  process  is  the  formation  of  AgCN2~ 
from  Ag+  and  2CN~,  a  process  which  involves  the  loss  of  one 
positive  and  one  negative  charge.  The  mass  law  requires  that 

(Ag(CN)Q-       K 

(Ag+)(CN)2- 

K  is  here  a  constant  which  is  a  numerical  expression  for  the 
tendency  of  the  complex  ion  to  form  and  may  be  designated  as  the 
"  complex  ion  constant."  In  this  example  it  has  a  very  large  value, 
namely,  1  X  1021,  and  hence  the  reaction  is  irreversible. 


CHAPTER  VII 

METHODS   OF  PRODUCING  AND   APPLYING  HEAT 

Sources  of  Heat  Used.  Many  quantitative  operations  depend 
for  their  success  upon  the  maintenance  of  definite  temperatures 
for  either  long  or  short  time  intervals.  The  range  of  temperatures 
used  is  wide,  and  a  great  number  of  devices  become  desirable  or 
necessary  if  efficiency  and  speed  are  to  be  attained.  Altho  it  costs 
less  under  normal  conditions  to  produce  heat  by  the  consumption 
of  gas  than  of  electrical  energy,  the  latter  method  is  more  directly 
and  easily  controlled,  and  frequently  the  difference  in  cost  is  more 
than  offset  by  the  greater  certainty  with  which  it  can  be  used,  and 
the  absence  of  undesirable  gaseous  decomposition  products. 

Heating  with  an  Electric  Current.  The  amount  of  heat  pro- 
duced by  the  passage  of  a  current  through  a  resistor  varies  with 
the  product  of  the  resistance  offered  and  the  square  of  the  current 
transmitted,  and,  therefore,  depends  upon  the  current  strength 
to  a  greater  extent  than  the  resistance.  Various  materials  are 
used  as  resistors  in  constructing  devices  for  this  purpose;  the 
most  convenient  are  certain  alloys,  such  as  German  silver,  monel 
metal,  and  nichrome,  which  possess  a  high  specific  resistance,  a 
high  melting  point  and  ability  to  resist  oxidation  at  high  tempera- 
tures. The  alloy  last  named  possesses  all  of  these  properties  to 
a  maximum  degree  and  can  be  obtained  at  small  cost  in  wire  or 
ribbon  of  any  desired  size. 

In  constructing  an  electric  heating  device  the  factors  of  greatest 
importance  are  the  voltage  of  the  current  available,  which  may  be 
either  direct  or  alternating,  the  masses  and  specific  heats  of  the 
substances  used  in  its  construction,  the  losses  from  radiation,  and 

60 


METHODS  OF  PRODUCING  AND  APPLYING  HEAT         61 


the  temperature  which  it  is  desired  to  attain.  If  the  voltage  is 
fixed  the  length  and  size  of  the  wire  used  as  a  resistor  are  the 
essential  features  to  be  decided  on,  and,  owing  to  the  large  number 
of  variables  concerned,  this  must  be  determined  by  experiment 
rather  than  by  calculation.  It  may  be  noted,  however,  that  a 
long  piece  of  coarse  wire  forms  a  more  durable  resistor  than  a  short 
piece  of  fine  wire  which  has  an  equal  resistance.  The  temperature 
attained  with  such  devices  is  fairly  constant  so  long  as  the  voltage 
and  radiation  losses  are  constant.  It  can  be  reduced  by  reducing 
the  voltage,  and  is,  therefore,  easily  regulated,  that  is  for  tempera- 
tures attained  with  the  maximum  voltage,  by  introducing  a  rheo- 
stat in  the  circuit. 

Devices  Used  for  Evaporation.  The  evaporation  of  solutions 
rarely  necessitates  the  use  of  temperatures  greatly  in  excess  of 
100°.  Temperatures  somewhat  below  this  point,  but  sufficient 
for  the  evaporation  of  most  aqueous  solutions,  are  conveniently 
attained  by  the  use  of  a  "  steam  bath,"  that  is,  a  vessel  in  which 
water  is  made  to  boil  vigorously,  either  by  a  coil  of  steam  pipes  or 
by  the  flame  of  a  gas  burner,  and  which  has  a  cover  provided  with 
openings  for  the  receptions  of  the  vessels  containing  the  solutions 
to  be  evaporated.  A  bath  of  a  sufficient  size  to  accommodate  a 
large  number  of  such  vessels  is  an  essential  part  of  the  equipment 
of  a  quantitative  laboratory.  It  has 
the  great  advantage  of  keeping  the 
solutions  at  a  uniform  temperature 
well  below  the  point  at  which  mechan- 
ical losses  are  to  be  anticipated. 

Direct  heating  of  the  vessel  contain- 
ing the  solution  by  a  flame  is  usually 
avoided  by  interposing  a  plate  of 

metal,  forming  a  " hot-plate,"  or  a 

£ii   j     -XL,         j  £  j  Fig.  7.  —  Sand  Bath 

tray  filled  with  sand,  forming  a    sand- 
bath,"  between  the  flame  and  the  vessel.     A  sand-bath  of  this 
character  is  represented  in  Fig.  7.     It  gives  a  higher  temperature, 


62 


QUANTITATIVE   CHEMICAL  ANALYSIS 


and  therefore,  more  rapid  evaporation  i/han  the  steam-bath,  and 
can  be  controlled  by  varying  the  gas  supplied  to  the  burner  or  the 
thickness  of  the  layer  of  sand  used.  It  is  especially  useful  where 
the  liquid  is  retained  in  a  flask  and  gentle  ebullition  is  not 
objectionable. 

When  it  becomes  necessary 
to  attain  still  higher  tempera- 
tures, as  in  the  evaporation  of 
sulfuric  acid,  the  vessel  contain- 
ing the  substance  to  be  evapor- 


Fig.  8.  —  Asbestos  Muffle  Fig.  9.  —  Air  Bath 

ated  may  be  placed  inside  a  "muffle,"  that  is,  an  outer  shell  which 
protects  the  inner  vessel  from  the  flame  and  permits  it  to  be  heated  by 
radiation  only.  A  large  nickel  or  iron  crucible  can  be  used  as  a  muffle 
for  this  purpose,  but  the  device  represented  in  Fig.  8,  which  is  made 
of  heavy  asbestos  board  and  bound  with  sheet  iron  is  more  durable. 
Devices  for  Drying  Solids.  The  amount  of  vapor  to  be  ex- 
pelled in  drying  solids  is  usually  small,  as  compared  with  that 
expelled  in  evaporating  liquids,  and  the  apparatus  used  may  take 
the  form  of  a  rectangular  oven,  such  as  is  represented  in  Fig.  9. 


METHODS  OF  PRODUCING  AND  APPLYING  HEAT        63 


Its  temperature  can  be  roughly  regulated  by  varying  the  height 
of  the  flame  or  the  size  of  the  burner  by  which  it  is  heated;  if 
greater  refinement  is  necessary  an  automatic  gas-regulator,  which 
increases  or  decreases  the  gas  supply  as  the  temperature  falls  below 
or  exceeds  that  for  which  the  regulator  is  set,  can  be  used.  Ovens 
of  larger  size  which  are  used  for  cooking  and  can  be  obtained  from 
hardware  dealers,  can  often  be  used  to  advantage. 

Still  another  device,  represented  in  Fig.  10,  consists  of  a  double- 
walled  oven,  in  which  the  intervening  space  is  filled  with  a  liquid 
whose  boiling  point  is  slightly 
above  the  temperature  desired. 
This  liquid  is  kept  at  the  boiling 
point  by  means  of  a  burner,  and 
the  vaporized  liquid  is  condensed 
and  returned  to  the  oven  as 
fast  as  produced.  The  liquids 
most  frequently  used  are  water, 
which  gives  a  temperature  of 
about  96°,  and  toluene  which  gives 
a  temperature  of  nearly  105°.  In 
all  devices  of  the  oven  type  the 
water  vapor  which  is  generated 
escapes  but  slowly  and  their  effi- 
ciency, that  is,  the  rate  at  which 
drying  is  affected,  is  not  great.  Fig.  10.- Constant-temperature  Oven 

A  further  objection  to  ovens  heated  by  gas  is  that  some  of  the 
combustion  products  may  enter  the  oven  and  produce  objection- 
able effects  upon  the  substance  being  dried.  For  this  reason  the 
electrically  heated  ovens,  which  can  now  be  purchased  from 
dealers  in  chemical  apparatus,  are  to  be  preferred  to  all  others; 
their  cost,  however,  is  somewhat  large. 

Temperatures  Attainable  by  the  Use  of  Gas  Burners.  Direct 
heating  of  the  substance  in  a  crucible  is  always  to  be  preferred 
where  there  is  no  danger  of  exceeding  the  maximum  permissible 


64 


QUANTITATIVE  CHEMICAL  ANALYSIS 


temperature.  The  temperature  actually  attained  inside  of  the 
crucible  depends  upon  the  type  of  burner  used,  the  calorific  value 
of  the  gas  burned,  and  the  masses  and  specific  heats  of  the  sub- 
stances heated,  that  is,  the  crucible  used,  the  triangle  used  to 
support  it,  and  the  substance  which  it  contains. 

The  Bunse.n  burner  is  decidedly  inferior  to  the  more  recently 
devised  Meker  burner,  a  vertical  projection  of 
which  is  represented  in  Fig.  11.  In  the  former  the 
air  supplied  at  the  base  is  not  sufficient  for  the 
gas  burned  and  a  long  cone-shaped  flame  results; 
the  area  over  which  active  combustion  takes  place 
is  comparatively  large,  and  the  highest  temperature 
is  attained  at  the  apex  of  the  inner  blue  cone.-  In 
the  Meker  burner  the  air  supplied  at  the  base  is 
sufficient,  but  " striking  back"  is  prevented  by  the 
grid  and  enlargement  at  the  outlet;  the  entire 
combustion  takes  place  within  a  few  millimeters 
of  the  top  of  the  grid,  and  the  heating  effect  is 
therefore  concentrated  in  a  single  horizontal 
plane. 

The  temperatures  actually  attained  in  the  in- 
terior of  uncovered  crucibles  of  different  sizes 
and  materials,  which  were  heated  on  triangles  of  nichrome 
wire  by^the  two  forms  of  burners  are  given  in  the  following 
table : 


Fig.  11.— M6ker 
Burner 


Berlin 

Berlin 

Berlin 

Crucible  heated 

porcelain 

porcelain 

porcelain 

Platinum 

00 

0 

1 

Capacity 

10  cc. 

15  cc. 

23  CC. 

14  CC. 

29  cc. 

Temperature  with    Bun- 

sen  burner 

820° 

780° 

720° 

840° 

780° 

Temperature  with  Meker 

burner  

880° 

840° 

770° 

890° 

805° 

METHODS  OF  PRODUCING  AND  APPLYING  HEAT         65 


Somewhat  higher  temperatures  are  attained  by  using  covers  on 
the  crucibles,  but  this  prevents  the  circulation  of  air  within  the 
crucible  and  the  escape  of  gases  which  may  be  liberated  by  the 
substance  heated  in  the  crucible,  both  of  which  effects  are  unde- 
sirable. 

Still  higher  and  more  uniform  temperatures  can  be  reached 
by  surrounding  the  burner  and  crucible  with  a  shield,  which  cuts 
off  air-currents  and  greatly  reduces  the 
radiation  losses.  This  device  is  utilized 
in  the  burner  devised  by  Chaddock,  a 
vertical  projection  of  which  is  repre- 
sented in  Fig.  12.  Combustion  of  the 
gas  used  is  effected  exactly  as  in  the 
Bunsen  burner,  but  the  entire  burner 
is  made  of  porcelain,  and  a  fire-clay 
chimney  which  fits  upon  it  loosely  both 
reduces  the  losses  from  radiation  and 
forms  a  support  for  a  triangle  over 
which  a  crucible  can  be  heated. 

Where  still  higher  temperatures  are 
needed  a  "  blast  lamp,"  that  is,  a 
burner  which  is  supplied  with  a  blast 


of  air,   or  an  electric  furnace  can  be  Fig.  12. -Chaddock  Burner 
used.     An   effective  blast  lamp  is  ca- 
pable of  producing  a  temperature  of  1100°  in  a  platinum  crucible 
of  moderate  size. 

Construction  of  an  Electric  Furnace.  Small  electric  furnaces 
designed  to  heat  crucibles  of  moderate  size,  which  can  be  pur- 
chased from  dealers,  are  extremely  advantageous.  The  plan  of 
an  inexpensive  and  easily  constructed  furnace  is  represented  in 
vertical  and  horizontal  projection  in  Fig.  13.  The  heating  unit 
consists  of  an  alundum  core  (A)  two  inches  in  diameter,  around 
which  is  wound  15  feet  of  No.  23  nichrome  wire  coiled  in  the  form 
of  a  helix  four  feet  long  and  one-eighth  of  an  inch  in  diameter. 


66 


QUANTITATIVE  CHEMICAL  ANALYSIS 


The  core  and  helix  rest  upon  a  piece  of  asbestos  board  supported 
^^^xx^^x^  r;x>^>>x>>^////^i  by  a  ring  of  porcelain  (B);  it  is 

placed  in  the  center  of  a  cylinder 
of  sheet  copper  some  four  inches 
in  diameter,  which  is  supported 
in  a  vertical  position  by  means 
of  a  wooden  base  (C);  but  is 
insulated  from  the  base  by  strips 
of  thick  asbestos.  The  entire 
space  between  the  core  and  cyl- 
inder is  filled  with  a  compact 
mass  of  asbestos.  The  ends  of 
the  helix  are  brought  thru  but 
insulated  from  the  copper  cylin- 
der and  attached  to  binding  posts 
screwed  into  the  base. 

When  this  furnace  is  attached 
to  a  110-volt  circuit  it  consumes 
about  3  amperes  of  current. 
When  a  crucible  is  placed  in- 
side the  core  and  the  furnace  is 
covered,  the  temperature  inside 
the  crucible  rapidly  rises  to 
1000°.  A  lower  temperature  can 
be  attained  by  placing  a  rheo- 
stat in  series  with  it,  but  it  is 


Fig.  13. — Plan  of  an  Electric  Furnace  more  economical  to  construct 
other  furnaces  which  offer  a  greater  resistance  where  lower  tem- 
peratures are  desired. 


CHAPTER  VIII 

THE   REMOVAL   OF  UNDESIRABLE   CONSTITUENTS   BY 
EVAPORATION 

Factors  to  be  Considered.  It  is  frequently  necessary  to  re- 
duce the  volume  of  the  solution  containing  the  substance  being 
analyzed  or  to  eliminate  certain  volatile  constituents  by  evapora- 
tion. The  factors  which  determine  the  rate  at  which  evaporation 
takes  place  are  the  vapor  pressure  of  the  solution  at  different 
temperatures,  the  rate  at  which  the  vapor  formed  is  carried  away 
from  the  surface  of  the  liquid,  the  extent  of  this  surface  and, 
where  the  temperature  used  is  that  of  the  boiling  point,  upon  the 
efficiency  of  the  heating  device  employed.  The  phenomenon  of 
boiling  is  due  to  the  fact  that  bubbles  of  vaporized  liquid  are 
constantly  forming  at  the  bottom  or  in  the  interior  of  the  mass  of 
liquid  and  passing  to  its  surface;  these  bubbles  are  often  pro- 
jected above  the  surface  of  the  liquid  with  considerable  violence, 
and  may  carry  with  them  small  quantities  of  the  solution  being 
evaporated.  Hence,  unless  a  special  form  of  apparatus  is  used, 
which  prevents  the  escape  of  these  particles,  appreciable  losses 
of  the  non-volatile  constituents  of  the  solution  may  occur.  This 
difficulty  is  somewhat  intensified  by  the  phenomenon  of  "  super- 
heat ing/7  in  which  portions  of  the  liquid  which  are  in  immediate 
contact  with  the  bottom  of  the  containing  vessel  are  temporarily 
heated  above  the  normal  boiling  point  and  then  suddenly  vapor- 
ized; it  can  be  avoided  by  agitating  the  liquid,  or  by  adding  to  it  a 
small  piece  of  platinum  wire  or  some  other  good  conductor  of  heat. 

If  a  mixture  of  a  solid  and  a  liquid  is  being  evaporated  the 
phenomenon  known  as  " bumping'7  may  occur.  It  is  due  to  the 

67 


68  QUANTITATIVE   CHEMICAL  ANALYSIS 

fact  that  the  solid,  especially  when  it  has  a  high  specific  gravity, 
packs  together  on  the  bottom  of  the  containing  vessel,  and  bubbles 
of  vapor  accumulate  between  this  layer  and  the  bottom  of  the 
vessel.  Their  pressure  finally  overcomes  that  of  the  layer  and 
in  escaping  they  throw  masses  of  the  mixture  out  of  the  vessel  with 
considerable  violence.  This  difficulty  does  not  arise  if  the  tem- 
perature is  kept  somewhat  below  the  boiling  point,  or  if  the  mixture 
is  stirred  vigorously. 

Evaporation  can  be  greatly  hastened  by  sucking  the  vapor 
formed  from  the  containing  vessel  by  means  of  a  suction  pump, 
or  by  directing  a  current  of  air  against  the  surface  of  the  liquid  by 
means  of  a  force  pump.  Either  device  cools  the  surface  appreci- 
ably, but  as  a  more  efficient  heating  device  can  then  be  used,  the 
rate  of  evaporation  can  be  greatly  increased. 

Methods  of  Effecting  Evaporation.  Two  extremes  are  repre- 
sented in  the  methods  used  to  effect  rapid  evaporations.  Either 
the  liquid  is  placed  in  a  shallow  evaporating  dish  and  heated  to  a 
temperature  somewhat  below  its  boiling  point,  or  it  is  placed  in  a 
flask  or  narrow  beaker  and  boiled  violently.  The  latter  method 
is  somewhat  more  rapid  but  requires  care  and  watchfulness  on  the 
part  of  the  analyst,  and  is  always  subject  to  the  possibility  of 
small  mechanical  losses.  Where  the  former  method  is  used,  a 
heating  device  which  permits  of  a  rapid  and  constant  control  of 
the  temperature  is  necessary.  Direct  heating  over  a  flame,  even 
though  the  vessel  is  protected  from  it  by  a  piece  of  wire  gauze,  is 
not  to  be  recommended.  The  use  of  a  water  or  " steam  bath," 
which  insures  a  temperature  somewhat  below  100°,  is  usually  very 
satisfactory.  A  sand  bath,  or  a  hot  plate  give  higher  temperatures 
and  more  rapid  evaporation  but  involve  possibilities  of  mechanical 
losses. 

Evaporation  of  Mixtures  of  Two  Volatile  Substances,  When 
two  substances,  which  possess  appreciable  vapor  pressures  and 
form  homogeneous  solutions,  are  mixed  together  a  reduction  in 
the  vapor  pressures  of  both  constituents  takes  place,  and  the  sum 


REMOVAL  OF  UNDESIRABLE  CONSTITUENTS 


69 


of  the  vapor  pressures  of  the  two  constituents  in  the  mixed  vapor 
phase  is  less  than  the  sum  of  the  vapor  pressures  of  the  pure  sub- 
stances at  the  same  temperature.  The  extent  to  which  one  con- 
stituent of  such  a  mixture  lowers  the  vapor  pressure  of  the  other, 
varies  with  different  pairs  of  liquids,  but  all  known  examples  be- 
long to  one  of  three  types.  These  types  can  be  differentiated  most 
readily  by  plotting  the  curves  representing  the  total  vapor  pres- 
sures of  the  two  constituents  in  the  mixed  phase  corresponding  to 
all  possible  mixtures  of  these  constituents.  Such  curves  are  repre- 
sented in  Fig.  14,  in  which  the  ordinates  represent  vapor  pressures, 


<\          10         20         30        40         50         60         70          80         90         B 

Fig.  14.  —  Curves  Representing  Vapor  Pressures  of  Mixed  Liquids 

and  the  abscissas  the  comparative  amounts  of  the  two  constituents 
A  and  B.  In  type  I  the  total  vapor  pressure  of  the  mixture  in- 
creases continuously  from  a,  corresponding  to  the  pure  constituent 
A,  to  fr,  corresponding  to  the  pure  constituent  B.  In  type  II  the 
total  vapor  pressure  attains  a  minimum  value  at  p,  that  is,  it  is 
reduced  by  adding  B  to  pure  A  or  A  to  pure  B  up  to  the  concentra- 
tion which  yields  the  minimum  value  p.  In  type  III  the  total 
pressure  attains  a  maximum  value  at  q,  that  is,  it  is  increased  by 
adding  B  to  pure  A  or  A  to  pure  B  up  to  the  concentration  which 


70  QUANTITATIVE   CHEMICAL  ANALYSIS 

gives  the  maximum  value  q.  Since  the  boiling  points  of  such  mix- 
tures depend  directly  upon  the  sum  of  vapor  pressures  of  the  two 
constituents  the  boiling  points  of  mixtures  representing  type  I 
decrease  continuously  as  the  percentage  of  that  constituent  which 
has  the  greater  vapor  pressure  increases;  whereas  the  boiling 
points  of  mixtures  representing  type  II  attain  a  maximum  and 
those  of  type  III  attain  a  minimum  at  certain  concentrations  of 
the  two  constituents.  If  then  mixtures  belonging  to  type  II  are 
continuously  evaporated  the  composition  of  the  mixture  changes 
up  to  the  point  at  which  it  has  the  maximum  boiling  point;  those 
representing  type  III  must  change  up  to  the  point  at  which  it  has 
the  minimum  boiling  point.  Mixtures  which  are  characterized 
by  constant  boiling  points  yield  mixed  vapor  phases  in  which  the 
relative  amounts  of  the  two  constituents  are  the  same  as  in  the 
corresponding  liquid  phases. 

Removal  of  Acids  by  Evaporation.  The  mixtures  of  this  kind 
which  are  most  frequently  dealt  with  in  quantitative  work  are 
aqueous  solutions  of  acetic,  hydrochloric,  nitric  and  sulfuric  acids; 
the  first  three  of  these  mixtures  belong  to  type  II.  The  rate  at 
which  any  one  of  these  acids  is  driven  out  of  an  aqueous  solution 
thru  evaporation  depends  mainly  upon  the  concentration  of  that 
acid  in  the  mixed  vapor  phase.  Useful  data  can  therefore  be 
secured  by  evaporating  aqueous  solutions  of  these  .acids  at  their 
boiling  points,  condensing  and  collecting  the  vapor  given  off  at 
definite  time  intervals,  and  determining  the  composition  of  the 
condensed  liquid  and  of  the  solutions  from  which  they  were  dis- 
tilled. The  results  of  a  series  of  determinations  *  of  this  kind  are 
given  in  the  curves  of  Fig.  15.  The  ordinates  represent  the  per- 
centages of  the  various  acids  in  the  distillates  and  the  abscissas 
those  of  the  acids  in  the  corresponding  solutions. 

These  curves  at  once  show  the  comparative  volatilities  of  the 
different  acids  and  the  concentrations  which  must  be  attained 
before  they  can  be  driven  out  with  even  reasonable  rapidity  by 
*  From  experimental  data  obtained  by  the  writer. 


REMOVAL  OF  UNDESIRABLE  CONSTITUENTS 


71 


evaporation.  It  will  be  noted  that  in  evaporating  solutions  of 
acetic  acid  the  concentration  of  the  liquid  increases  at  a  uniform 
rate  until  the  residual  solution  contains  about  80  per  cent.  Solu- 


100 

9 


o  45 

dfl 

£  40 


2  35 


H  .N 


H2SC) 


H(C2H 


0       5      10    15    20    25    30    35    40    45    50    55    60    65   70    75    80    85   90    95    100 
Percentage  of  Acid  in  Solution 

Fig.  15.  —  Curves  Showing  the  Changes  in  Concentration  which  Result 
when  Dilute  Acids  are  Distilled 

tions  of  hydrochloric  acid  concentrate  very  rapidly  at  first,  then 
more  slowly  until  a  mixture  which  has  a  constant  maximum  boil- 
ing point  of  110°,  and  contains  20.2  per  cent  of  acid  is  obtained. 
The  behavior  of  nitric  acid  resembles  that  of  hydrochloric,  but  the 
constant-boiling  mixture  contains  68  per  cent  of  acid,  and  boils 
at  120°.  Sulfuric  acid  on  the  other  hand  is  not  appreciably  vola- 
tilized until  the  solution  has  attained  a  concentration  of  about  98 


72  QUANTITATIVE  CHEMICAL  ANALYSIS 

per  cent,  which  requires  a  temperature  of  more  than  250°.  Com- 
plete removal  of  any  of  these  acids  cannot  be  effected  unless  the 
solution  is  evaporated  to  dryness;  the  total  amount  left  in  any 
solution  which  has  been  concentrated  to  a  constant  boiling  point 
mixture  can  be  calculated  from  the  volume  left  and  the  composition 
of  this  mixture. 

The  theory  of  the  removal  of  acids  from  solutions  containing 
two  or  more  acids  is  not  so  easily  followed,  for,  altho  the  addition 
of  a  second  acid  reduces  the  volatility  of  the  first,  interaction 
between  the  two  acids  may  take  place.  Thus  when  both  hydro- 
chloric and  nitric  acids  are  present  a  reaction  represented  by  the 
equation  given  below  becomes  possible: 

HN03  +  3  HC1  -*  NOC1  +  2  H20  +  C12. 

The  reaction  constant  has  a  relatively  small  value,  and  unless  the 
concentrations  of  the  two  acids  are  large  but  little  chlorine  is 
liberated.  At  high  concentrations  and  especially  at  moderately 
high  temperatures  the  NOC1  formed  breaks  down  into  NO  and 
CL,  and  complete  decomposition  and  expulsion  of  the  acid  which 
is  not  present  in  excess  is  rapidly  effected.  Hence  it  is  possible 
to  expel  either  acid  by  adding  an  excess  of  the  other  acid,  and 
evaporating  the  solution  sufficiently. 


CHAPTER  IX 

THE   CALCULATION   OF  RESULTS 

Calculation  of  Chemical  Factors.     The  general  formula  for 
the  calculation  of  the  results  of  any  direct  gravimetric  process  is 

Weight  of  substance  separated  v 

^T  .  T, — * —  -  X  /  X  100  =  desired  percentage. 

Weight  of  sample  used 

In  this  formula  /  represents  the  factor  by  which  the  weight  of  the 
separated  substance  must  be  multiplied  to  give  the  equivalent 
weight  of  the  substance  whose  percentage  is  to  be  reported.  Since 
the  substance  weighed  and  the  substance  reported  may  have  the 
same  chemical  formula,  /  may  have  the  value  1 ;  usually  it  has 
a  different  value,  which  may  be  either  greater  or  less  than  1, 
and  can  be  calculated  from  the  atomic  and  molecular  weights  of 
the  substances  concerned.  If  a  precipitate  of  Mg2p207  has  been 
separated,  and  it  is  desired  to  report  the  percentage  of  P  present, 
it  would  be  reasoned  that  every  molecule  of  Mg2P207  separated 
represents  two  atoms  of  P  in  the  sample,  and  hence  the  desired 
factor  is  obtained  by  dividing  two  times  the  atomic  weight  of 
phosphorus  by  the  molecular  weight  of  magnesium  pyrophosphate. 
If  a  precipitate  of  Fe203  has  been  separated,  and  it  is  desired  to 
report  the  Fe30i  present,  the  reasoning  would  be  that  for  every 
three  molecules  of  Fe203  found,  two  of  Fe3C>4  must  have  been 
present  and  the  proper  factor  to  employ  is  2  Fe3C>4  -=-  3  Fe203. 
It  should  be  especially  noted  that  the  number  and  character  of 
the  reactions  concerned  in  the  production  of  the  substance  which 
is  separated  from  the  sample  are  of  no  significance.  When  a 
substance  which  contains  Fe304  is  analyzed  by  separating  Fe203 

73 


74  QUANTITATIVE  CHEMICAL  ANALYSIS 

from  it,  it  can  be  assumed  that  since  the  process  is  a  quantitative 
one  all  of  the  iron  present  as  Fe304  is  transformed  into  Fe2O3,  and 
further,  that  no  additional  iron  in  any  form  is  introduced. 

Determination  of  Chemical  Factors  Experimentally.  The 
value  of  /  can  also  be  determined  experimentally  by  submitting 
a  sample  containing  a  known  percentage  of  the  substance  which 
is  to  be. reported  upon  to  the  process  concerned,  and  calculating  the 
ratio  of  the  weight  of  the  substance  known  to  be  present  in  the 
sample  used  to  the  weight  of  product  separated.  An  empirically 
determined  factor  of  this  kind  is  subject  to  errors  of  the  same  kind 
and  magnitude  as  those  concerned  in  the  actual  determination. 
If  the  process  is  a  complex  one,  in  which  subsidiary  reactions  are 
possible,  and  large  errors  of  any  kind  are  to  be  expected,  the 
empirically  determined  factor  is  the  logical  one  to  use,  for  by  using 
it  the  errors  involved  in  the  actual  determination  are  partly  or 
wholly  counterbalanced.  If  the  process  is  based  upon  a  few  simple 
and  definite  reactions  and  is  not  subject  to  any  large  errors  the 
calculated  factor  should  be  used,  since  it  is  based  upon  experi- 
mental work  of  much  greater  accuracy  than  that  employed  in  the 
determination  of  the  empirical. factor. 

The  System  of  Atomic  Weights  Used.  The  atomic  weights 
of  the  various  elements  are  calculated  with  respect  to  the  atomic 
weight  of  hydrogen  with  a  value  of  1,  or  with  respect  to  that 
of  oxygen  with  a  value  of  16.  The  actual  ratio  of  the  atomic 
weights  of  these  elements  is  1.008  :  16  and  hence,  the  systems 
based  upon  the  two  standards  differ  slightly.  In  calculating  the 
factors  used  in  analytical  chemistry  either  system  may  be  used  with 
equal  accuracy  provided  all  the  weights  made  use  of  are  referred 
to  the  same  system  and  with  about  equal  facility.  The  atomic 
weights  which  will  be  used  in  this  book  are  those  adopted  by  the 
International  Committee  on  Atomic  Weights  in  1914. 

Form  in  Which  Results  Are  Reported.  The  form  in  which  the 
results  of  an  analysis  is  reported  admits  of  some  degree  of  choice, 
which  depends  largely  upon  the  object  for  which  the  analysis  is 


THE   CALCULATION  OF  RESULTS 


75 


Element 

Sym- 
bol 

Atomic 
weight 

Element 

Sym- 
bol 

Atomic 
weight 

Aluminum 

Al 

27   10 

Mercury 

Hg 

200  6 

Antimony  .  .  . 

Sb 

120  20 

Molybdenum  

Mo 

96  00 

Arsenic 

As 

74  96 

Nickel 

No 

58  68 

Barium 

Ba 

137  37 

Nitrogen  

N 

14  01 

Bismuth 

Bi 

208  00 

Oxygen 

o 

16  00 

Boron 

B 

11  00 

Phosphorus  

P 

31  04 

Bromine  

Br 

79.92- 

Platinum  

Pt 

195.20 

Cadmium 

Cd 

112  40 

Potassium     

K 

39  10 

Calcium  

Ca 

40.07 

Selenium  

Se 

79.20 

Carbon 

C 

12  00 

Silicon     .  . 

Si 

28  30 

Chlorine  .  .  . 

Cl 

35.46 

Silver    

Ag 

107.88 

Chromium 

Cr 

52  00 

Sodium 

Na 

'23  00 

Cobalt  

Co 

58  97 

Strontium  

Sr 

87.63 

Copper  

Cu 

63.57 

Sulfur  

S 

32.07 

Fluorine 

F 

19  00 

Tellurium  

Te 

127  50 

Gold  

Au 

197.20 

Thallium  

Tl 

204.00 

Hydrogen 

H 

1  008 

Tin 

Sn 

119  00 

Iodine  

I 

126.92 

Titanium  

Ti 

48.10 

Iron 

Fe 

55  84 

Tungsten 

W 

184  00 

Lead  .  . 

Pb 

207  10 

Uranium  

u 

238.50 

Lithium  

Li 

6.94 

Vanadium  

V 

51.00 

Magnesium 

Mg 

24  32 

Zinc                 .    .  . 

Zn 

65.37 

Manganese  

Mn 

54.93 

Zirconium  

Zr 

90.60 

made.  In  general,  it  is  advisable  to  report  all  results  in  such  a 
form  as  will  indicate  most  nearly  the  actual  composition  of  the 
sample.  Thus,  if  nitrogen  is  determined  and  reported  as  such, 
there  is  no  means  of  knowing  which  one  of  the  various  forms  in 
which  that  element  may  be  combined  is  represented,  whereas  if 
the  report  is  in  terms  of  NH3,  N2O5  or  N203,  the  presence  of  corre- 
sponding percentages  of  ammonia,  of  nitrates  or  of  nitrites  is 
clearly  shown.  Since  bxygen,  unless  it  is  in  the  free  condition, 
is  but  rarely  determined  it  is  customary  to  combine  it  with  the 
metals  or  metalloids  actually  present  in  the  report  made.  This 
makes  it  readily  possible  to  show  the  degree  of  oxidation  of  these 
elements  and  to  account  for  everything  present,  that  is,  to  make 
the  analysis  sum  up  to  100  per  cent.  Thus  in  the  analysis  of 


76  QUANTITATIVE  CHEMICAL  ANALYSIS 

crystallized  ferrous  sulfate  it  is  desirable  to  report  the  percentages 
of  FeO,  S03  and  H2O. 

It  should  be  noted  that  if  salts,  such  as  chlorides  or  sulfides, 
which  do  not  contain  oxygen,  are  present,  and  all  of  the  bases 
present  are  reported  as  oxides,  more  oxygen  will  be  included  in 
the  summation  than  is  actually  present.  The  proper  correction 
is  then  made  by  subtracting  the  oxygen  equivalent  of  the  chlorine 
and  sulfur  from  the  summation;  this  then  appears  in  the  summary 
as  "less  oxygen  due  to  chlorine  and  sulfur/' 

When  a  solution  is  submitted  to  analysis  it  is  now  customary  to 
report  the  ions  present.  Formerly  an  attempt  was  made  to  cal- 
culate and  report  the  probable  salts  present,  that  is,  to  combine 
the  acidic  and  basic  radicals  according  to  certain  arbitrary  rules. 
This  method  is  misleading  if  the  validity  of  the  electrolytic  dis- 
sociation theory  is  granted. 

Abbreviation  of  Calculations.  Altho  the  calculations  of  ana- 
lytical chemistry  involve  simple  multiplications  and  divisions  only 
it  will  be  found  advantageous  to  make  use  of  logarithms  or  of  a 
slide  rule.  Where  a  large  number  of  determinations  are  made  by 
the  same  process  and  the  same  chemical  factor  is  used,  time  can 
be  saved  by  preparing  a  table  showing  the  values  of  those  multiples 
of  this  factor  which  may  be  needed  most  frequently.  Still  another 
method  of  arriving  at  the  same  result  is  to  plot  a  curve,  in  this 
case  a  straight  line,  showing  the  relation  between  this  factor  and 
certain  multiples  of  it.  Many  handbooks  containing  tables  of 
this  kind  and  other  information  frequently  needed  by  the  analyt- 
ical chemist  have  been  prepared.* 

Another  device  which  is  sometimes  used  is  to  employ  "factor 
weights77  in  making  the  analysis.  If  the  quantity  of  sample 
employed  is  made  equal  to  /  of  the  general  formula  the  desired 
percentage  is  exactly  100  times  the  weight  of  the  separated  sub- 

*  Van  Nostrand's  Chemical  Annual  by  J.  C.  Olsen;  Chemists7  Pocket 
Manual  by  R.  Meade;  Chemical  and  Metallurgical  Handbook  by  Cremer 
and  Bicknell;  Conversion  Tables  for  Iron  Analysis,  by  Allen. 


THE  CALCULATION  OF  RESULTS  77 

stance.  If  the  factor  weight  is  larger  or  smaller  than  it  is  desirable 
to  use,  a  simple  fraction  or  multiple  of  it  can  be  used  with  nearly 
equal  advantage. 

Calculation  of  Chemical  Formulae.  The  analytical  chemist 
is  sometimes  required  to  calculate  the  probable  formula  of  an 
unknown  substance  from  the  results  of  his  analysis.  If  each  of 
the  percentages  obtained  are  divided  by  the  respective  atomic  or 
molecular  weights,  a  series  of  figures  are  obtained  which  repre- 
sent the  relative  number  of  atoms  or  molecules  present  in  the 
molecule  whose  formula  is  sought.  The  numbers  actually  ob- 
tained will  not  usually  be  entire  integers  and  some  of  them  may 
be  less  than  unity.  Since  no  chemical  formula  which  involves  the 
use  of  fractions  is  permissible  it  becomes  necessary  to  multiply  or 
divide  the  entire  series  by  a  factor  which  will  most  nearly  reduce 
them  all  to  whole  numbers.  The  simplest  method  of  procedure  is 
to  first  note  which  of  the  series  has  the  smallest  value,  and  to 
divide  the  entire  series  by  this  value.  The  results  represent  the 
simplest  formula  which  can  be  assigned  to  the  substance;  the  cor- 
rect formula  cannot  be  calculated  unless  the  molecular  weight  is 
also  known. 

For  example  the  analysis  of  an  unknown  mineral  gave  the  series 
of  figures  which  appear  in  the  first  column  given  below: 

K20  =  15.41  -^  94.3    =  0.1634  1.00 

MgO  =    6.58  4-  40.36  =  0.1630  1.00 

CaO  =  18.80  -f-  56.10  =  0.3351  -f-  0.163  =  2.05 

S03  =  52.91  -4-  80.07  =  0.6597  4.05 

H2O  =  5.84    ~  18.02  =  0.3241  1.99 

Dividing  by  the  proper  molecular  weights  gives  the  figures  which 
appear  in  the  third  column,  and  dividing  these  by  0.163  those  of 
the  last  column.  The  simplest  probable  formula  of  the  mineral  is 
therefore  K2MgCa2(S04)4  •  2  H20,  which  represents  the  mineral 
polyhalite. 


SECTION  II 
GAS-EVOLUTION  PROCESSES 


CHAPTER  X 

GENERAL  FEATURES   OF   GAS-EVOLUTION   PROCESSES 

The  Decomposition  of  Carbonates.  The  simplest  examples 
of  this  class  of  determinations  are  those  in  which  the  formation  of 
a  gaseous  product  is  effected  by  a  change  in  temperature.  The 
determination  of  carbon  dioxide  in  certain  carbonates  furnishes  a 
good  illustration.  The  decomposition  of  calcium  carbonate  is 
expressed  by  the  reaction 

CaC03 ->  CaO  +  C02. 

The  system  here  represented  consists  of  two  solid  phases,  each  of 
which  is  a  pure  substance  and  therefore  has  a  constant  concentra- 
tion, and  a  gas  phase,  the  composition  of  which  can  vary.  Since 
the  concentrations  of  CaC03  and  CaO  in  the  solid  phases  are  con- 
stant the  concentrations  of  these  substances  in  the  gas  phase 
must  remain  constant  so  long  as  appreciable  amounts  of  the  two 
solids  are  present.  Hence  in  representing  the  conditions  which 
determine  the  equilibrium  between  all  three  substances  in  the  gas 
phase  the  constant  concentrations  of  the  CaO  and  CaC03  can  be 
assumed,  and  the  concentration  of  C02,  which  is  proportional  to 
the  equilibrium  constant,  can  be  used  in  place  of  the  latter;  hence 
for  all  practical  purposes  we  can  write 

K  =  (C02). 

The  concentrations  of  gases  in  a  gaseous  mixture  are  propor- 
tional to  the  partial  pressures  which  they  exert,  and  therefore  the 

78 


GENERAL  FEATURES  OF  GAS-EVOLUTION  PROCESSES      79 


value  of  K  can  also  be  expressed  in  terms  of  pressure,  most  con- 
veniently as  the  number  of  millimeters  of  mercury  to  which  that 
concentration  corresponds.  When  so  expressed  the  mass  law 
states  that  equilibrium  is  determined  in  all  such  reactions  by  the 
partial  pressure  of  the  C02  in  the  gas  phase  by  which  the  two  solids 
are  surrounded.  If  the  pressure  of  carbon  dioxide  in  the  gas  phase 
is  less  than  K,  the  reaction  progresses  from  left  to  right;  if  this 
pressure  is  greater  than  K  it  progresses  from  right  to  left.  The 
value  of  K,  when  so  expressed,  is  known  as  the  "  dissociation 
pressure"  of  the  substance  which  undergoes  decomposition,  it 
represents  the  only  pressure  at 
which  carbon  dioxide  is  in  equi- 
librium with  both  CaC03  and 
CaO  at  the  given  temperature. 
The  effect  of  varying  temper- 
ature upon  the  dissociation 
pressures  of  the  carbonates  of 
calcium,  lithium  and  barium  is 
shown  in  Fig.  16;  in  all  cases 
the  value  of  K  increases  very 
rapidly  with  increasing  temper- 
ature. As  the  concentration  of 
C02  in  air  of  normal  composi- 
tion corresponds  to  a  pressure 
represented  by  a  very  small 
fraction  of  a  millimeter  of  mer- 
cury, it  should  be  possible  to 


P  in  mm  of  Mercury 
CaCOs                   Li2CO3      BaCO 

on 

80 
70 
60 
50 
40 
30 
20 
10 

T 

1 

\ 

1 

\ 

I 

/ 

1 

1 

I 

_t 

/ 

/ 

T_ 

—  ** 

y 

s/ 

ooo       ooo       o      o       o 
ooo       ooo       o      o      o 

Fig.  16.  —  The  Dissociation  Pressures 
of  Carbonates 


effect  complete  decomposition  of  all  the  carbonates  named,  by 
heating  them  to  easily  attainable  temperatures,  provided  the  car- 
bon dioxide  produced  is  not  permitted  to  accumulate  in  the  gas 
surrounding  the  sample.  If  the  samples  are  heated  in  covered 
vessels  the  decomposition  would  be  incomplete  unless  the  tem- 
perature was  raised  above  the  point  at  which  the  pressure  of  the 
liberated  carbon  dioxide  exceeded  that  of  the  atmosphere,  that  is, 


80  QUANTITATIVE  CHEMICAL  ANALYSIS 

of  760  mm.  This  would  require  a  temperature  in  excess  of  825° 
for  calcium  carbonate  and  of  1450°  for  barium  carbonate. 

It  might  also  be  noted  that  by  careful  control  of  the  tempera- 
ture and  carbon  dioxide  pressure  it  should  be  possible  to  analyze 
certain  mixtures  of  such  carbonates.  If  a  mixture  of  calcium 
and  barium  carbonates  is  heated  to  constant  weight  in  a  stream 
of  pure  carbon  dioxide  to  a  temperature  slightly  in  excess  of  825° 
the  loss  in  weight  is  an  accurate  measure  of  the  amount  of  cal- 
cium carbonate  present;  if  next  heated  above  1450°  the  loss  in 
weight  is  an  accurate  measure  of  the  barium  carbonate  present. 

The  Dehydration  of  Salts.  A  second  illustration  of  this 
class  of  processes  is  found  in  the  method  universally  used  for  the 
determination  of  the  water  present  in  hydrated  salts.  Such  de- 
terminations are  based  upon  reversible  reactions,  which  can  be 
represented  by 

Hydrated  salt  —  >  anhydrous  salt  +  water  vapor. 

As  the  hydrated  and  anhydrous  salts  are  present  as  pure  solid 
phases  their  concentrations  are  constant,  and  the  very  slight 
concentrations  in  the  vapor  phase  to  which  they  give  rise  are  also 
constant.  Hence  the  equilibrium  in  the  vapor  phase,  which  de- 
termines the  equilibrium  in  the  entire  system,  becomes  simply 


in  which  P  represents  the  maximum  vapor  pressure  corresponding 
to  the  water  vapor  present  in  the  gas  phase,  when  equilibrium  has 
been  attained.  The  relation  between  K  and  the  partial  pressure 
of  the  water  vapor  in  the  gas  by  which  the  salt  is  surrounded  de- 
termines the  direction  in  which  the  reaction  progresses.  If  this 
concentration  is  kept  smaller  than  K  by  passing  a  current  of  dry 
gas  over  the  salt,  it  is  dehydrated;  if  this  concentration  is  kept 
greater  than  K,  the  salt  takes  up  water. 

Many  salts  are  able  to  form  a  series  of  hydrates  each  of  which 
contains  a  definite  number  of  molecules  of  water,  and  are  not 


GENERAL  FEATURES  OF  GAS-EVOLUTION  PROCESSES     81 


stable  unless  the  concentration  of  the  water  vapor  by  which  they 
are  surrounded  lies  between  certain  limits,  which  vary  with  the 
temperature.  The  complete  dehydration  of  such  salts  is  repre- 
sented by  a  series  of  reactions. 

The  Dehydration  of  Crystallized  Copper  Sulfate.  This  salt, 
which  contains  five  molecules  of  water,  is  stable  under  ordinary 
atmospheric  conditions,  because  the  partial  pressure  of  the  water 
vapor  normally  present  in  the  atmosphere  exceeds  the  dissociation 
pressure  of  this  hydrate  at  20°.  By  increasing  the  temperature 
or  reducing  the  concentration 
of  the  water  vapor  surrounding 
the  salt  a  series  of  reactions 
resulting  in  the  formation  of 
CuS04  •  3  H20,  CuS04  •  H20  and 
CuS04,  can  be  made  to  take 
place.  The  conditions  necessary 
to  effect  these  different  trans- 
formations are  indicated  by  the 
series  of  curves  shown  in  Fig. 
17,  in  which  the  ordinates  rep- 
resent water-vapor  pressures 
and  the  abscissas  temperatures. 
The  curve  CO  indicates  the 
series  of  temperatures  and  pres-  Fig.  17.  — Vapor  Tensions  of  Hydrates 
sures  at  which  the  penta-  and  of  Copper  SuKate 

trihydrate  are  in  equilibrium;  DO  those  at  which  the  tri-  and 
monohydrates  are  in  equilibrium;  and  EO  those  at  which  the 
monohydrate  and  the  anhydrous  salt  are  in  equilibrium.  The 
space  between  CO  and  DO  represents  the  only  series  of  conditions 
at  which  the  trihydrate  is  stable,  that  between  DO  and  EO  the 
only  conditions  under  which  the  monohydrate  is  stable,  and  that 
below  EO  the  only  conditions  under  which  the  anhydrous  salt  is 
stable.  Complete  dehydration  can  be  effected  within  the  range  of 
conditions  represented  by  the  field  EOY. 


82  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  Evolution  Method.  The  weight  of  the  gas  liberated  by 
such  reactions  as  those  under  discussion  can  often  be  estimated 
by  determining  the  total  loss  in  weight  of  the  apparatus  in  which 
the  reaction  takes  place,  that  is,  by  determining  the  weight  of 
liberated  gas  by  the  "  evolution  method."  In  general,  there  are 
two  extremes  represented  in  the  method  of  procedure  adopted. 
In  one  the  temperature  is  kept  very  high,  and  no  attempt  made 
to  reduce  the  partial  pressure  of  the  liberated  gas  below  that 
normally  present;  in  the  other  the  temperature  is  kept  low,  and 
the  partial  pressure  of  the  liberated  gas  is  artificially  reduced. 
Where,  owing  to  volatilization  of  the  residual  product  or  to  other 
changes  which  affect  its  weight,  the  maximum  temperature  which 
can  be  used  is  too  low  to  cause  complete  and  rapid  decomposition 
of  the  sample,  it  is  desirable  or  even  necessary  to  reduce  the  partial 
pressure  of  the  liberated  gas  by  passing  a  current  of  air,  or  some 
other  gas,  over  the  sample.  This  necessitates  the  use  of  a  some- 
what elaborate  apparatus  similar  to  that  used  for  the  direct 
method  described  in  the  next  paragraph. 

The  Absorption  Method.  Since  the  residual  compound  is 
often  hygroscopic,  and,  therefore,  difficult  to  weigh,  and  since  it 
is  sometimes  impossible  to  entirely  avoid  reactions  involving 
changes  in  weight  in  addition  to  the  one  desired,  it  is  sometimes 
necessary  to  pass  the  liberated  gas  into  an  apparatus  which 
absorbs  it  completely,  and  determine  its  weight  by  the  direct  or 
"  absorption  method/7  The  decomposition  must  then  be  made  in 
a  closed  vessel  and  all  of  the  liberated  gas  washed  thru  the  absorb- 
ing apparatus  by  means  of  a  current  of  air,  or  some  other  gas 
which  contains  no  substances  which  are  also  taken  up  by  the 
absorbing  apparatus. 

When  the  liberated  gas  is  to  be  determined  by  the  absorption 
method,  or  when  a  gas  is  to  be  passed  over  the  substance  to  be 
analyzed  and  determined  by  the  evolution  method,  an  apparatus 
similar  to  the  one  represented  in  Fig.  18  becomes  necessary.  This 
consists  of  a  cylindrical  muffle  of  sheet  nickel  or  monel  metal 


GENERAL  FEATURES  OF  GAS-EVOLUTION  PROCESSES     83 


supported  horizontally  on  four  legs  and  enclosing  a  glass  tube, 
the  diameter  of  which  is  sufficiently  large  to  contain  a  porcelain 
"boat,"  which  holds  the  substance  to  be  analyzed.  The  tem- 


Fig.  18.  —  Muffle  Furnace  for  Heating  Tubes 


perature  of  the  air  space  within  the  muffle,  which  is  somewhat 

higher  than  that  of  the  substance  within  the  boat,  can  be  measured 

with  a  thermometer.     It  is  possible  to  heat  the  substance  in  such 

an  apparatus   by  means  of   a    single   Bunsen 

burner  up  to  as  high  as  350°  and  where  the 

danger  of  exceeding  the  maximum  permissible 

temperature  is  but  small,  an  opening  can  be 

made  in  the  bottom  of  the  muffle  and  the  tube 

heated  directly,  even  up  to  the  point  at  which 

the  glass  begins  to  soften.     Where  still  higher 

temperatures  are  necessary,  a  tube  of  porcelain 

should  be  used. 

The  absorption  of  the  liberated  gas  can  be 
effected  in  several  types  of  apparatus,  which  should  be  as  light 
and  compact  as  possible.      For  solid  absorbents  a  U  tube,  as 
represented  in  Fig.  19,  is  most  convenient;   for  liquid  absorbents 
a  U-tube  containing  pieces  of  pumice  stone  saturated  with  the 


Fig.    19. —  Glass- 


84 


QUANTITATIVE   CHEMICAL  ANALYSIS 


liquid,  or  certain  special  forms  of  absorption  bulbs  such  as  that  of 
Geissler,  Fig.  20,  can  be  used. 

General  Theory  When  the  Reagent  Is  a  Gas.     Reactions  re- 
sulting in  the  liberation  of  a  gas,  which  are  brought  about  by  the 

addition  of  a  reagent,  form  the  basis  of 
many  useful  quantitative  processes. 
The  reagent  itself  may  be  a  gas,  in 
which  case  the  system  concerned  is  one 
involving  equilibrium  between  one  or 
more  solid  phases  and  a  mixed  gas 
phase.  The  method  of  " combustion" 
invariably  used  for  the  determination 
of  carbon  and  hydrogen  in  organic  com- 
pounds is  representative  of  this  class. 
They  involve  reactions  similar  to 

Fig.  20.  —  Geissler  Bulb         Ci2H22On  +  12  02  ->  12  C02  +11  H20. 
The  expression  for  equilibrium  in  this  reaction  is 


K  = 


(02)1 


Evidently  all  reactions  of  this  type  can  be  made  irreversible  by 
keeping  the  concentrations  of  the  gases  formed  low  and  that  of 
the  gaseous  reagent  used  high.  This  is  easily  effected  by  use  of 
the  apparatus  already  described,  that  is,  by  placing  the  substance 
to  be  analyzed  in  a  narrow  tube,  and  passing  the  gas  used  as  a 
reagent  over  it. 

General  Theory  When  the  Reagent  Is  a  Liquid.  When  the  re- 
agent used  is  a  liquid,  the  system  concerned  involves  equilibrium 
between  a  liquid,  a  gas  and  a  solid,  as  for  example,  in  the  reaction  : 


CaC03  +  2  H+ 


-  ->  Ca++ 


~  +  H20  +  C02 


If  we  disregard  the  concentration  of  water,  which  in  the  solutions 


GENERAL   FEATURES  OF   GAS-EVOLUTION   PROCESSES      85 

usually   used   remains  practically   constant,   the   expression   for 
equilibrium  reduces  itself  to 

(Ca++)  •  (CO,) 


K  = 


(H+)2 


Evidently  such  reactions  can  be  made  irreversible  if  the  concen- 
tration of  the  reagent  used  can  be  made  sufficiently  large,  and  the 
solubility  of  the  liberated  gas  can  be  made  sufficiently  small. 

The  weight  of  the  liberated  gas  can  be  determined  by  the 
evolution  method,  the  absorption  method,  or  by  direct  measure- 
ment of  its  volume,  and  calculation  of  the  corresponding  weight. 
For  the  evolution  method  a  large  number  of  special  forms  of 
apparatus,  which  are  known  as  alkalimeters,  can  be  employed. 
One  of  these  is  represented  in  Fig.  23,  in  which  A  represents  the 
receptacle  which  contains  the  substance  to  be  analyzed,  and  in 
which  the  reaction  takes  place,  B  the  receptacle  for  the  reagent 
used,  and  C  the  receptacle  for  the  reagent  used  to  dry  and  purify 
the  liberated  gas.  The  weight  of  the  entire  apparatus  as  first 
charged  with  sample  and  reagents,  and  again  after  the  reaction 
has  been  completed,  is  accurately  determined;  the  difference  gives 
the  desired  weight  of  the  liberated  gas. 

For  the  absorption  method  an  apparatus  similar  to  the  one 
represented  in  Fig.  24  is  used.  The  essential  features  are  again 
a  container  for  the  reagent,  a  container  for  the  substance  to  be 
analyzed,  which  also  serves  as  the  vessel  in  which  the  reaction 
takes  place,  one  or  more  absorbing  tubes  by  which  the  liberated 
gas  is  dried  and  purified,  and  an  absorption  apparatus  containing 
the  proper  reagents  for  the  retention  of  the  gas  which  is  to  be 
weighed. 

General  Theory  When  the  Reagent  Is  a  Solid.  The  salts  of 
certain  acids,  especially  H2C03,  HC1,  HNO3  and  HC103,  are 
completely  decomposed  with  the  liberation  of  a  gas  by  heating 
them  with  certain  oxides  such  as  Si02  or  B2O3,  or  with  certain  acid 
salts  such  as  Na2B407.  A  typical  illustration  is  furnished  by  the 


86  QUANTITATIVE  CHEMICAL  ANALYSIS 

reaction  between  sodium  paratungstate  and  potassium  nitrate, 
which  is  represented  by 

NaioWi204i  +  14  KN03  ->  5  Na2W04  +  7  K2W04  +  7  N205. 

Since  both  of  the  substances  which  are  concerned  in  such 
reactions  are  solid  at  ordinary  temperatures,  it  is  necessary  to  raise 
the  temperature  of  the  mixture  to  the  point  at  which  one  or  both 
of  them  is  partly  or  wholly  fused  in  order  to  insure  complete  inter- 
action; hence  the  factors  which  determine  the  reversibility  of  such 
reactions  are  the  same  as  those  which  determine  the  reversibility 
of  the  reactions  considered  in  the  preceding  paragraph.  As  most 
of  the  processes  of  this  class  can  be  carried  out  by  heating  a 
known  weight  of  the  sample  with  a  known  weight  of  the  reagent  in 
an  open  crucible  they  are  extremely  simple  and  in  many  cases 
extremely  accurate. 


CHAPTER  XI 

DETERMINATION   OF  WATER  IN   GYPSUM -^ 
I    FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Composition  of  Gypsum.  The  composition  of  this  mineral  is 
represented  by  the  formula  CaS04  •  2  H20.  It  is  frequently  found 
in  the  form  of  colorless,  transparent  and  beautifully  crystalline 
masses,  which  are  practically  free  from  other  minerals  and  mechani- 
cally occluded  impurities  of  all  kinds,  and  which  contain  the 
theoretical  percentage  of  water. 

Conditions  for  Dehydration.  The  complete  dehydration  of 
gypsum  is  expressed  by  means  of  two  reactions,  namely: 

2  CaS04  •  2  H20  -»  2  CaS04  •  H20  +  2  H20 
2CaS04-H20    ->2CaS04-t^H20. 

The  pressures  of  water  vapor  at  which  gypsum  is  in  equilibrium 
with  the  hemihydrate  and  with  anhydrous  calcium  sulfate  (soluble 
anhydrite)  have  been  found  to  be  as  follows : 

30°        50°          70°     90° 

Gypsum  and  hemihydrate  12.70    50          161 

Gypsum  and  soluble  anhydrite         16 .10     59 . 90     188    446 

When  gypsum  is  placed  in  a  loosely  covered  vessel  and  the  tem- 
perature slowly  raised  a  large  amount  of  water  is  rapidly  expelled 
at  1<50°  and  a  smaller  amount  at  2®$.  The  first  temperature  is 
the  point  at  which  the  vapor  pressure  of  the  dihydrate  exceeds 
that  of  one  atmosphere,  the  second  that  at  which  the  hemihydrate 
exceeds  that  of  one  atmosphere. 

The  only  other  decomposition  involving  a  change  in  weight, 

87 


88  QUANTITATIVE  CHEMICAL  ANALYSIS 

which  can  result  from  a  change  in  temperature  produces  either 
calcium  oxide  or  a  basic  calcium  sulfate  and  sulfur  trioxide. 
Neither  of  these  changes  take  place  until  a  temperature  of  at  least 
500°  is  reached. 

Possible  Sources  of  Error.  If  gypsum  is  heated  rapidly  it 
sometimes  shows  a  tendency  to  "boil,"  that  is,  the  sudden  con- 
version of  the  chemically  combined  water  into  steam  rends  the 
larger  masses  into  extremely  fine  particles,  and  this  may  lead  to 
an  appreciable  mechanical  loss.  The  difficulty  can  be  avoided 
entirely  by  heating  slowly  until  most  of  the  water  is  expelled, 
preferably  in  a  deep  vessel,  and  by  reducing  the  size  of  the  particles 
of  which  the  sample  is  composed.  Care  must  be  taken,  however, 
to  avoid  long-continued  grinding,  as  it  has  been  shown  that  this 
may  result  in  the  loss  of  appreciable  amounts  of  water,  probably 
owing  to  the  heat  developed  by  friction. 

Properties  of  Anhydrous  Calcium  Sulfate.  When  gypsum  is 
dehydrated  below  a  temperature  of  512°  the  so-jcalled  "soluble 
anhydrite"  is  obtained;  if  heated  above  this  temperature  "insol- 
uble anhydrite"  is  formed.  The  former  salt  is  not  only  much 
more  soluble  but  also  much  more  hygroscopic  than  the  latter.  In 
determining  the  water  in  gypsum  by  the  evolution  method  several 
milligrams  of  water  may  be  absorbed  while  the  residue  of  soluble 
anhydrite  is  being  weighed,  unless  the  determination  is  made  in  a 
vessel  which  can  be  closed  by  means  of  a  tightly  fitting  stopper. 
As  the  maximum  temperature  needed  is  250°  a  glass  weighing- 
bottle  can  be  used,  altho  it  must  be  heated  somewhat  slowly  in  a 
muffle  or  an  electric  furnace  to  prevent  cracking.  Satisfactory 
results  can  also  be  obtained  by  heating  in  a  covered  porcelain  or 
platinum  crucible,  but  some  experience  is  necessary  to  weigh  the 
residual  salt  with  sufficient  speed. 

The  determination  can  be  made  with  about  equal  accuracy  by 
the  absorption  method,  that  is,  by  collecting  and  weighing  the 
liberated  water,  but  this  requires  a  more  elaborate  apparatus  and 
takes  more  time. 


DETERMINATION  OF  WATER  IN  GYPSUM 


89 


II.   DETAILS  OF  METHOD  OF  PROCEDURE 

Preparing  and  Weighing  Out  Sample.  Crush  several  grams 
of  the  air-dry  sample  in  a  clean  mortar  until  the  resulting  grains 
are  about  the  size  of  a  pin  head,  and  transfer  to  a  clean,  dry 
"sample  tube";  that  is,  a  test  tube  about  1  cm.  in  diameter 
and  8  cm.  long,  which  is  provided  with  a  good  cork  stopper. 

Procure  a  weighing  bottle  of  not  more  than  20  cc.  capacity, 
clean  carefully  and  wipe  both  inner  and  outer  surfaces  with  a  dry 
cloth,  then  allow  to  stand,  preferably  in  the  balance  room,  for 
twenty  minutes  or  until  it  has  taken  up  the  normal  amount  of 
moisture  from  the  air.  Weigh  the  bottle 
and  cover  accurately  to  within  0.5  mg. 
Remove  the  cover,  and  add  about  2  gm. 
of  the  prepared  sample,  and  again  cover 
and  weigh  accurately  to  within  0.2  mg. 

Dehydration.  Procure  a  nickel  crucible 
of  some  50  cc.  capacity,  cut  a  circular 
piece  of  wire  gauze  slightly  larger  than 
the  bottom  of  the  crucible,  ignite  it  over 
a  flame,  and  place  in  the  crucible  as 
shown  in  Fig.  21.  Cut  a  piece  of  asbestos 
cloth  of  slightly  smaller  size  and  place  on 
top  of  the  gauze.  Support  the  crucible 
on  a  piece  of  wire  gauze  which  is  placed  ^8-  21-  —  Apparatus  for 
some  two  inches  above  the  top  of  a  Bunsen  : 
burner,  then  remove  the  cover  from  the  weighing  bottle  and  place 
the  bottle  inside  the  crucible.  Heat  the  gauze  with  a  low  flame 
for  ten  minutes,  then  gradually  increase  the  gas  supplied  until  the 
wire  gauze  under  the  muffle  is  heated  to  dull  redness,  and  keep 
at  this  temperature  for  a  half  hour,  but  do  not  let  the  gas  take 
fire  and  burn  above  the  gauze.  The  temperature  attained  inside 
the  muffle  should  be  about  250°;  it  can  be  measured  by  means  of  a 
mercury  thermometer  suspended  as  shown  in  the  figure. 


90  QUANTITATIVE  CHEMICAL  ANALYSIS 

Weighing  the  Residual  Salt.  Shut  off  the  gas,  place  the  cover 
in  position  and  allow  the  muffle  to  cool  for  about  three  minutes, 
then  transfer  the  bottle  to  a  piece  of  paper,  wood  or  some  poor 
conductor  of  heat;  and  after  a  few  minutes,  place  in  the  balance 
room  and  allow  to  remain  for  twenty  minutes.  If  the  hot  bottle 
is  brought  into  contact  with  a  piece  of  cold  metal  or  any  other 
good  conductor  of  heat  it  is  certain  to  crack.  Weigh  the  bottle 
to  within  0.2  mg. ;  if  it  shows  any  tendency  to  increase  in  weight 
while  on  the  balance  pan  allow  it  to  stand  for  another  ten 
minutes  and  again  weigh.  Finally  place  the  bottle  in  the  muffle, 
heat  as  before  for  ben  minutes,  and  again  cool  and  weigh.  If  the 
difference  between  the  two  weighings  does  not  exceed  0.3  mg. 
the  dehydration  of  the  sample  can  be  assumed  to  be  complete. 
Calculate  the  percentage  of  water  present. 

III.   FURTHER  DETAILS  REGARDING  THE  ANALYSIS 

Meaning  of  Percentage  Error.  In  discussing  the  accuracy  of 
quantitative  processes  care  should  be  taken  to  distinguish  between 
"  percentage  error "  and  what  will  be  designated  in  this  book  as 
"  departure/'  Percentage  error  always  means  the  error  for  every 
one  hundred  parts  of  the  substance  determined;  departure,  the 
difference  between  the  correct  percentage  and  the  percentage 
reported.  Thus,  if  a  substance  contains  exactly  70  per  cent  of  a 
certain  constituent  and  69.8  is  found  by  analysis,  the  departure 
is  70  -  69.8  =  0.2,  but  the  percentage  error  is  100  (70  -  69.8) 
•v-  70  =  0.285.  The  difference  between  departure  and  percentage 
error  becomes  zero  when  the  substance  analyzed  contains  100  per 
cent  of  the  constituent  reported.  In  general  the  percentage  error 
of  a  quantitative  process  should  be  expected  to  increase  somewhat 
as  the  percentage  reported  on  decreases,  but  in  neither  case  is  the 
one  change  proportional  to  the  other. 

Accuracy  of  Method.  The  determination  outlined  above  rep- 
resents an  ideal  quantitative  process,  as  regards  both  simplicity 
and  accuracy.  The  entire  estimation  can  be  made  within  two 


DETERMINATION   OF  WATER  IN   GYPSUM  91 

hours,  and  the  results  should  not  differ  from  the  theoretical  figure 
by  more  than  one-tenth  of  a  per  cent  if  the  work  is  carefully 
executed.  The  accuracy  of  the  method  can  be  still  further  in- 
creased by  increasing  the  amount  of  sample  used,  altho  the  time 
needed  for  complete  dehydration  is  thereby  increased. 

IV.  QUESTIONS  AND  PROBLEMS.     SERIES  2 

/  1.  Calculate  the  percentage  error  of  your  determination  of  water  in  gyp- 
sum. If  the  same  percentage  error  was  made  in  determining  the  water  in  a 
salt  containing  60  per  cent  of  water  what  result  would  you  obtain? 

/  2.  If  2  gm.  of  the  sample  were  used  in  making  the  determination  as  directed 
and  the  only  errors  involved  were  a  plus  error  of  1  mg.  in  weighing  the  empty 
bottle  and  a  plus  error  of  0.2  mg.  in  weighing  the  bottle  and  residue  after  igni- 
tion, what  departure  would  be  obtained?  If  the  only  errors  involved  were  a 
plus  error  of  0.2  mg.  in  weighing  the  empty  bottle,  and  a  plus  error  of  1  mg. 
in  weighing  the  bottle  and  residue,  what  departure  would  be  obtained? 
*  3.  What  weight  of  water  is  present  in  1  liter  of  air  saturated  at  50°  and 
760  mm.,  assuming  that  the  partial  pressure  of  water  vapor  at  this  temper- 
ature is  92  mm.  and  that  a  liter  of  water  vapor  at  0°  weighs  0.803  gm.? 

4.  If  2  gm.  of  gypsum  was  heated  to  90°  in  a  vacuous  space  which  has  a 
volume  of  500  cc.  until  equilibrium  has  been  established,  how  much  gypsum 
would  remain?  Jtt.<jt>°  -  ^^6  n*>.»m  ~  e^./-^«*  of  *at*r  „«{ 

r  5.  How  would  you  determine  the  water  in  a  mixture  of  calcium  carbonate 
and  gypsum? 

6.  What  difficulties  would  you  anticipate  if  the  method  used  for  the  deter- 
mination of  water  in  gypsum  was  used  for  the  compound  CaCl2  •  6  H2O, 
Mg(NO3)2  •  6  H2O,  FeSO4  •  7  H2O,  ZnSO4(NH4)2SO4  •  6  H2O? 

7.  If  1  gm.  of  a  mixture  of  two  carbonates  lost  0.15  gm.  when  heated  to 
900°  and  .1292  gm.  when  heated  to  1200°,  what  carbonates  are  present,  and 
what  are  theTpercentages  of  each?     (For  data  see  page  80.) 


CHAPTER  XII 

DETERMINATION  OF  WATER  IN  CRYSTALLIZED  COPPER  SULFATE 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Purification  of  the  Salt.  When  copper  sulfate  is  purified  by 
recrystallization  the  pentahydrate  alone  separates  since  the  vapor 
pressure  of  the  solution  is  greater  than  that  of  this  hydrate  even 
if  the  temperature  of  the  saturated  solution  used  reaches  a  value 
of  50°.  The  separated  crystals  should  be  dried  by  pressing  them 
between  folds  of  filter  paper,  and  preserved  in  stoppered  bottles 
at  a  temperature  not  in  excess  of  25°.  The  salt  sold  by  reliable 
dealers  as  chemically  pure  usually  contains  very  nearly  the  theo- 
retical percentage  of  water. 

Conditions  Necessary  for  Dehydration.  Although  the  vapor 
pressure  exerted  by  even  the  monohydrate  of  copper  sulfate  at 
100°  exceeds  the  partial  pressure  of  water  vapor  normally  present 
in  the  atmosphere,  experience  shows  that  the  last  traces  of  water 
are  driven  off  from  this  salt  very  slowly  at  this  temperature.  As 
the  salt  does  not  begin  to  decompose  further  until  a  temperature 
of  341°  is  attained,  there  is  no  objection  to  dehydrating  at  200°, 
at  which  temperature  all  of  the  water  is  rapidly  and  completely 
expelled.  The  anhydrous  salt  is  extremely  hygroscopic,  and  altho 
the  method  used  for  the  determination  of  water  in  gypsum  can 
be  employed  in  this  case  also  the  more  widely  applicable  absorption 
method  will  be  described  here. 

The  Efficiency  of  Different  Dehydrating  Agents.  The  accu- 
racy of  the  absorption  process  for  the  determination  of  water 
depends  upon  the  efficiency  of  the  reagent  used  to  absorb  the 
liberated  water  vapor.  The  activity  of  all  such  reagents  depends 

92 


WATER  IN  CRYSTALLIZED  COPPER  SULFATE  93 

upon  their  capacity  to  combine  with  water,  and  is  large  in  pro- 
portion as  the  dissociation  pressure  of  the  compound  formed  by 
the  addition  of  water  is  small. 

Phosphorus  pentoxide  is  the  most  powerful  dehydrating  agent 
known,  which  is  due  to  the  fact  that  the  water-vapor  pressure  of 
the  phosphoric  acid  formed  is  practically  zero.  As  it  is  obtained 
in  the  form  of  a  fine  white  powder,  whose  surface  rapidly  becomes 
coated  with  an  impervious  layer  of  phosphoric  acid,  and  as  it  is  an 
expensive  reagent,  its  use  is  avoided  except  when  an  unusual 
degree  of  dehydration  is  necessary. 

Concentrated  sulfuric  acid  owes  its  power  to  the  formation  of 
a  series  of  liquid  hydrates,  which  are  miscible  with  water  in  all 
proportions.  The  vapor  pressure  of  the  concentrated  acid  is  but 
.little  less  than  that  of  phosphoric  acid ;  that  of  the  diluted  acid  in- 
creases rapidly  with  the  dilution.  It  has  been  measured  for  a  wide 
range  of  concentrations  at  a  number  of  temperatures  and  the  data 
obtained  is  extremely  useful  for  the  preparation  of  dehydrating 
reagents  of  specified  power.  The  gas  to  be  dehydrated  can  be 
passed  thru  tubes,  which  are  designed  to  hold  the  acid  in  liquid 
form,  or  thru  U-tubes  containing  pieces  of  pumice  stone  saturated 
with  it;  the  acid  in  such  tubes  must  be  renewed  frequently. 

Calcium  chloride  forms  a  series  of  hydrates,  all  of  which  are 
extremely  soluble.  It  is  to  be  had  from  dealers  in  two  forms. 
The  "fused"  salt  is  almost  anhydrous,  and  is  dense  and  heavy; 
the  " granular"  reagent,  if  fresh,  contains  from  15  to  20  per  cent 
of  water,  and  is  light  and  porous.  Its  dehydrating  power  decreases 
as  its  water  content  increases.  Samples  containing  from  14  to 
24  per  cent  of  water  (CaCl2  •  1  to  2  H20)  yield  a  vapor  pressure  of 
0.54  mm.;  those  containing  from  24  to  40  per  cent  (CaCl2-  2  to  4 
H20)  yield  a  pressure  of  1.47  mm.;  those  containing  from  40  to 
50  per  cent  (CaCl2  •  4  to  6  •  H20)  yield  a  pressure  of  2.47  mm.  The 
vapor  pressure  of  the  fused  salt  should  be  less  still,  but  its  action 
is  much  slower  than  that  of  the  lower  hydrates,  and  its  efficiency 
may  not  be  greater  unless  the  gas  to  be  dehydrated  is  passed  over 


94  QUANTITATIVE  CHEMICAL  ANALYSIS 

it  very  slowly.  Altho  the  granular  reagent  is  a  less  efficient 
dehydrating  agent  than  concentrated  su  If  uric  acid  the  fact  that 
it  can  be  obtained  in  the  form  of  a  light  porous  solid  makes  it  more 
convenient  to  use. 

The  Use  of  Granular  Calcium  Chloride.  If  the  partial  pres- 
sure of  the  water  vapor  in  the  air  passed  thru  the  apparatus 
during  the  determination  is  not  equal  to  or  less  than  the  vapor 
pressure  of  the  dehydrating  agent  used  to  retain  the  water  sep- 
arated from  the  sample  being  analyzed,  the  result  may  be  increased 
by  water  taken  up  from  the  air.  If  the  air  passed  thru  the  appa- 
ratus is  dehydrated  by  the  same  reagent  that  is  used  to  absorb 
the  water  liberated  from  the  sample  no  such  error  should  result. 
Under  these  conditions  also  no  error  should  result  from  the  use 
of  a  dehydrating  agent,  which  fails  to  remove  the  last  traces 
of  water  from  the  air  passed  thru  the  absorbing  tubes  since 
both  tubes  should  reduce  the  concentration  of  the  water  vapor 
to  the  same  value,  and  the  amount  of  water  taken  up  by  the  second 
absorbing  tube  represents  the  increase  in  the  concentration  of  water 
vapor  produced  by  the  decomposition  of  the  sample  under  analysis. 

Conditions  Necessary  for  Complete  Absorption.  If  the  liber- 
ated water  vapor  is  drawn  thru  the  absorbing  tube  too  rapidly 
some  of  it  may  not  be  retained.  If  the  air  current  used  is  not 
made  to  pass  continuously  in  the  proper  direction  some  of  the 
liberated  water  vapor  may  find  its  way  into  the  absorption  tube 
thru  which  the  air  enters.  A  steady  and  continuous  stream  of 
air  can  be  drawn  thru  the  apparatus  at  any  desired  rate  by  the 
use  of  an  " aspirator  bottle"  (E  of  Fig.  22).  If  air  enters  the 
apparatus  at  any  point  except  thru  the  tube  designed  to  purify 
it,  the  moisture  which  it  contains  may  be  absorbed  and  weighed 
with  the  separated  water.  Hence  the  joints  of  the  apparatus 
must  be  tight,  but  since  the  pressure  inside  and  outside  of  the 
apparatus  need  not  differ  much,  no  difficulty  should  be  experienced 
in  making  them  so. 

The  time  needed  for  the  determination  depends  largely  upon 


WATER  IN  CRYSTALLIZED  COPPER  SULFATE 


95 


the  amount  of  air  which  must  be  passed  thru  the  apparatus  to 
free  it  from  water  vapor  before  the  sample  is  heated,  and  also  to 
wash  the  separated  water  vapor  into  the  absorption  tube  after  the 
sample  has  been  decomposed;  it  increases,  therefore,  with  the 
capacity  of  the  apparatus,  which  should  be  made  as  small  as 

possible. 

II.   CONSTRUCTION  OF  THE  APPARATUS 

Procure  and  fit  together  the  parts  of  an  apparatus  similar  to 
that  shown  in  Fig.  22  as  follows: 

For  A  procure  a  simple  U-tube  about  18  cm.  in  length.  Clean 
and  dry  it  carefully  and  fill  with  lumps  of  dry  granular  calcium 


Fig.  22. —  Plan  of  Apparatus  for  Determination  of  Water 

chloride  of  about  the  size  of  a  pea.  Place  small  wads  of  cotton  on 
top  of  the  reagent  in  both  limbs  and  insert  in  the  two  ends  well- 
fitting  cork  stoppers  provided  with  an  inlet  and  outlet  tube 
respectively.  Prepare  also  two  "plugs"  by  inserting  short  pieces 
of  glass  rods  into  pieces  of  rubber  tubing  of  slightly  smaller  internal 
diameter,  and  use  to  cover  the  inlet  and  outlet  tubes,  and  thus 
protect  the  reagents  from  deterioration  when  the  tube  is  not  in  use. 
For  B  procure  a  piece  of  either  hard  or  soft  glass  tubing  about 
thirty  centimeters  long,  the  diameter  of  which  is  sufficient  to 
permit  the  insertion  and  removal  of  the  porcelain  boat  C  without 


96  QUANTITATIVE  CHEMICAL  ANALYSIS 

difficulty.  The  sharp  edges  at  the  end  of  the  tube  should  be 
rounded  off  by  heating  in  a  flame  until  they  begin  to  soften.  Pro- 
cure two  rubber  stoppers  which  fit  the  ends  of  the  tube  snugly  and 
are  bored  with  holes  for  the  admission  of  the  tubes  connecting 
with  A  and  D. 

For  D  procure  a  smaller  U-tube,  preferably  of  the  Marchand 
form,  in  which  one  limb  of  the  tube  is  sealed  directly  to  an  inlet 
tube  of  smaller  diameter,  the  latter  being  bent  at  right  angles  and 
provided  with  a  bulb-like  enlargement  near  the  middle  of  the 
horizontal  portion.  This  bulb  serves  to  condense  and  retain  a 
large  part  of  the  water  vapor  passing  thru  the  tube,  which  can  be 
poured  out,  or  removed  by  a  shred  of  filter  paper  after  the  tube 
has  been  used;  it  increases  the  number  of  determinations  that 
can  be  made  with  it  without  renewing  the  absorbing  reagent. 

Clean  and  dry  the  tube,  heating  it  in  an  air  bath  if  necessary  to 
expel  the  last  traces  of  water.  Insert  a  small  wad  of  cotton  just 
below  the  inlet  tube,  and  fill  with  pieces  of  granular  calcium 
chloride;  then  introduce  a  good  cork  stopper,  which  is  provided 
with  a  narrow  outlet  tube,  into  the  open  limb.  Place  a  few  small 
pieces  of  sealing  wax  upon  the  top  of  the  cork,  and  melt  these  by 
means  of  a  piece  of  hot  metal  till  the  cork  and  the  joint  between 
it  and  the  glass  are  covered  uniformly  and  smoothly.  Prepare 
well-fitting  plugs,  by  which  the  inlet  and  outlet  tubes  can  be  cov- 
ered, and  a  support  of  nickel  or  aluminum  wire  by  which  the  tube 
can  be  suspended. 

For  E  procure  an  aspirator  bottle  of  about  two  liters  capacity 
provided  with  an  exit  tube  which  can  be  easily  opened  or  closed 
by  means  of  a  screw  pinchcock. 

For  F  procure  a  thermometer  capable  of  indicating  temperatures 
of  300°. 

III.   DETAILS  OF  METHOD  OF  PROCEDURE 

Preliminary  Operations.  Prepare  the  sample  by  crushing 
several  grams  of  the  dry  crystalline  salt  to  a  fine  powder  in  a  clean 
agate  mortar  and  placing  in  a  clean,  dry  sample  tube. 


WATER  IN   CRYSTALLIZED   COPPER   SULFATE  97 

Ignite  the  porcelain  boat  by  holding  it  in  the  flame  of  a  burner, 
slightly  above  the  apex  of  the  inner  blue  cone,  for  a  few  minutes, 
then  place  in  a  desiccator  until  perfectly  cool,  which  should  re- 
quire about  twenty  minutes,  and  weigh  accurately  to  0.2  mg. 
Next  add  to  the  boat  about  1  gm.  of  the  sample  and  again 
weigh  accurately. 

Wipe  the  Marchand  tube  with  a  clean  dry  cloth,  place  it  in 
the  balance  room  for  twenty  minutes,  then  weigh  with  the  two 
plugs  in  position  accurately  to  within  0.3  mg.  If  the  tube  ap- 
pears to  gain  in  weight  while  on  the  balance  pan  it  must  be  allowed 
to  stand  longer,  that  is,  until  the  weight  is  constant. 

Assembling  the  Apparatus.  Connect  the  larger  U-tube  with 
the  combustion  tube  by  means  of  a  rubber  stopper.  Fill  the 
aspirator  bottle  with  water,  attach  it  directly  to  the  other  end 
of  the  combustion  tube  and  allow  about  200  cc.  of  water  to 
flow  out  rather  rapidly,  that  is,  within  a  period  of  about  ten 
minutes. 

Disconnect  the  aspirator  and  place  the  porcelain  boat  and  con- 
tents in  the  combustion  tube  at  the  point  indicated  in  the  figure. 
Connect  the  Marchand  tube  with  the  combustion  tube  by  means 
of  the  rubber  stopper,  taking  pains  to  press  it  firmly  into  place. 
Connect  the  aspirator  with  the  free  end  of  the  Marchand  tube  and 
adjust  the  pinch  cock  until  the  water  flows  from  it  at  a  rate  of 
about  two  drops  per  second,  and  maintain  this  rate  of  flow  during 
all  the  subsequent  operations. 

Decomposing  the  Hydrate.  Light  the  burner  under  the  muffle, 
and  allow  the  temperature  as  shown  by  the  thermometer  to  slowly 
rise  to  about  100°,  and  maintain  it  as  near  this  figure  as  possible 
for  twenty  minutes.  This  should  expel  four-fifths  of  the  water 
somewhat  rapidly;  decrepitation  may  take  place  but  does  no 
harm  as  the  residue  is  not  to  be  weighed.  Some  of  the  water 
may  condense  in  the  colder  portions  of  the  tube  just  outside  of  the 
muffle  and  it  may  be  necessary  later  to  heat  that  part  of  the  tube 
slightly,  by  changing  the  position  of  the  muffle,  but  this  must  be 


98  QUANTITATIVE  CHEMICAL  ANALYSIS 

watched  carefully,  or  small  amounts  of  water  vapor  or  sulfur  may 
be  expelled  from  the  rubber  stopper. 

Next  increase  the  height  of  the  flame  and  allow  the  temperature 
to  gradually  rise  to  200°  and  maintain  between  200°  and  250°  for 
twenty  minutes  longer.  At  the  expiration  of  this  period  the  residue 
in  the  boat  should  be  of  a  dead  white  or  slightly  gray  color;  if  it 
shows  a  tinge  of  blue  the  heating  should  be  continued  longer. 

Weighing  the  Liberated  Water.  Disconnect  the  aspirator, 
remove  the  Marchand  tube  and  cover  the  inlet  and  outlet  with 
the  proper  plugs,  place  in  the  balance  room  and  weigh  as  before. 
Remove  the  porcelain  boat  by  means  of  a  small  wire  hook  and  dis- 
connect and  cover  the  ends  of  the  larger  U-tube.  Calculate  the 
percentage  of  water  present. 

IV.   QUESTIONS  AND  PROBLEMS.     SERIES  3 

1.  Would  you  expect  the  sulfates  of  sodium,  zinc,  aluminum  and  iron, 
respectively,  to  decompose  into  the  corresponding  oxides  at  higher  or  lower 
temperatures  than  the  sulf ate  of  copper? 

2.  Ten  liters  of  moist  air  measured  at  20°  are  passed  thru  a  tube  filled  with 
calcium  chloride  containing  45  per  cent  of  water,  then  thru  a  tube  filled  with 
calcium  chloride  containing  18  per  cent  of  water,  what  weight  of  water  might 
be  taken  up  by  the  latter  tube? 

3.  A  saturated  solution  of  Na2HP04  is  placed  in  a  desiccator,  which  also 
contains  a  large  vessel  filled  with  65  per  cent  sulf  uric  acid  and  is  kept  at  30°. 
If   the  vapor  pressure  of   the  acid  is  7  mm.,  the   dissociation   pressure  of 

•  12  H2O  is  26  mm.,  that  of  Na2HPO4  •  7  H2O  is  18  mm.,  that  of 

•  2  H2O  is  2  mm.,  what  changes  would  take  place  in  both  solutions? 
What  difference  might  it  make  if  the  volume  of  the  Na2HPO4  solution  was 
large  and  that  of  the  H2SO4  solution  small?       OA 

4.  How  could  you  prove  that  copper  sulfate  formed  a  hydrate  having  the 
formula  CuSO4  •  3  H2O? 

5.  Calculate  the  probable  formula  of  a  hydrate  of  magnesium  sulfate  which 
was  found  to  contain  64.2  per  cent  of  water. 

6.  Show  how  the  data  given  by  Fig.  17  enables  you  to  determine  whether 
heat  is  absorbed  or  liberated  during  this  determination. 


CHAPTER  XIII 


DETERMINATION   OF   CARBON  DIOXIDE  IN  LIMESTONE  BY  THE 
EVOLUTION   METHOD 

I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Choice  of  Method.  The  value  of  a  sample  of  limestone  for 
many  purposes  is  determined  by  the  percentage  of  carbon  dioxide 
which  it  contains.  This  de- 
termination can  be  made  by 
ascertaining  the  loss  which 
takes  place  when  a  known 
weight  is  ignited  in  a  crucible, 
but  this  method  is  inaccurate 
if  the  sample  also  contains 
chemically  combined  water  or 
organic  matter.  When  these 
substances  are  present  the 
determination  can  be  rapidly 
made  by  the  evolution  method 
with  an  alkalimeter;  the  use  of 
the  Bunsen  alkalimeter  (see 
Fig.  23)  will  be  described  here. 
The  results  obtained  by  this 
method  should  not  differ  from 
the  correct  figure  by  more  than 
.2  per  cent. 

Possible  Sources  of  Error. 


Fig.  23.  —  Bunsen' s  Alkalimeter 
The  errors  involved  in  weighing 


a  Bunsen  apparatus  are  necessarily  somewhat  large  owing  to 
variations  in  the  amount  of  hygroscopic  water  which  condenses 

99 


100  QUANTITATIVE   CHEMICAL   ANALYSIS 

on  its  surface,  they  should  be  made  as  small  as  possible  by 
using  a  counterpoise  as  suggested  on  page  21.  The  use  of  a  large 
amount  of  sample  reduces  the  effect  of  this  error;  as  much  as  2  gm. 
can  be  used  to  advantage. 

The  carbon  dioxide  liberated  in  the  Bunsen  apparatus  is  satu- 
rated with  water  vapor  which  must  be  absorbed  before  the  gas  is 
permitted  to  escape.  Calcium  chloride  can  be  depended  upon  to 
remove  all  but  a  trace  of  water  from  the  escaping  gas,  provided 
the  escaping  gas  is  not  passed \ thru  the  absorbing  tube  too  rapidly. 
Some  samples  of  calcium  chloride  contain  small  amounts  of  cal- 
cium oxide  and  therefore  absorb  carbon  dioxide;  hence  the  calcium 
chloride  in  the  tube  C  should  be  saturated  with  carbon  dioxide 
before  it  is  used. 

Altho  the  reactions  between  the  carbonates  found  in  limestone 
and  either  dilute  hydrochloric  or  sulfuric  acids  are  practically 
complete,  the  solution  which  remains  after  the  decomposition  is 
saturated  with  carbon  dioxide,  and  to  this  extent  the  separation  of 
the  latter  is  incomplete.  If  a  moderate  excess  of  dilute  hydrochlo- 
ric acid  is  used  and  the  residual  solution  heated  slowly  to  about  50° 
practically  all  of  the  dissolved  carbon  dioxide  is  expelled,  and  there 
is  little  danger  of  expelling  either  acid  or  water  vapor. 

The  specific  gravity  of  carbon  dioxide  is  greater  than  that  of 
air  and  the  gas  retained  and  weighed  with  the  apparatus  after  use 
will  weigh  slightly  more  than  that  present  in  it  before  use,  unless 
a  sufficient  amount  of  air  is  drawn  through  it,  after  the  Decom- 
position has  been  completed.  This  air  should  be  dehydrated  by 
passing  it  thru  the  drying  tube  E,  otherwise  the  moisture  which 
it  contains  may  be  taken  up  by  the  drying  tube  C. 

II.   PREPARATION  OF  THE  APPARATUS 

Carefully  clean  the  three  parts  A,  B  and  C  of  a  Bunsen  apparatus 
(see  Fig.  23),  by  rinsing  with  acid  if  necessary,  then  with  water, 
allowing  them  to  drain  and  then  wiping  the  outer  surfaces  dry  with 


CARBON  DIOXIDE  IN  LIMESTONE  101 

a  clean  cloth.     Dry  the  inner  surface  of  the  tube  C  by  heating 
either  in  an  air  bath  or  very  cautiously  over  a  wire  gauze. 

Charge  the  drying  tube  by  placing  a  small  wad  of  cotton  in 
its  enlarged  end,  filling  to  within  1  cm.  of  the  other  end  with 
lumps  of  dry,  granular  calcium  chloride  of  about  the  size  of  a  pea, 
covering  with  a  second  wad  of  cotton,  and  closing  with  a  cork  of 
the  proper  size,  which  is  provided  with  an  inlet  tube  of  small 
diameter.  Press  the  cork  into  the  tube  till  flush  with  its  end  and 
cover  with  a  little  sealing  wax.  Pass  carbon  dioxide  from  a 
generator  thru  the  tube  for  about  twenty  minutes  and  displace  the 
excess  by  means  of  a  current  of  air. 

III.   DETAILS  OF  THE  METHOD  OF  PROCEDURE 

Charging  and  Assembling  the  Apparatus.  Prepare  a  long 
narrow  sample  tube,  which  is  small  enough  to  pass  into  the  flask 
A,  by  sealing  up  one  end  of  a  piece  of  thin-walled  glass  tubing  with 
a  flame  and  closing  the  other  with  a  cork,  and  charge  with  about 
2_gni.  of  the  sample.  Weigh  the  tube  accurately  and  deliver 
its  contents  without  loss  into  the  bottom  of  the  flask  A,  then 
withdraw  the  sample  tube  and  again  weigh  accurately. 

Pour  about  15  cc.  of  dilute  hydrochloric  acid  into  a  small  beaker, 
insert  the  shorter"oJ  the~two  tubes  attached  to  the  reservoir  tube 
B  into  the  acid  and  suck  up  about  10  cc.  of  the  acid,  then  remove 
the  tube  B  and  invert,  so  that  the  shorter  tube  again  stands  above 
the  acid.  Carefully  remove  the  acid  which  adheres  to  the  shorter 
tube  by  means  of  narrow  shreds  of  filter  paper. 

Next  unite  A,  B  and  C  as  shown  in  the  figure,  place  the  plugs 
D  and  Df  over  the  two  open  ends,  let  the  apparatus  stand  for  a 
half  hour  in  the  balance  room  and  weigh  accurately,  using  a  200  cc. 
flask,  which  has  also  stood  in  the  balance  room  during  the  previous 
half  hour,  as  a  counterpoise. 

Decomposing  the  Sample.  Remove  the  plugs  Dand  D'  and 
set  aside  where  they  can  not  be  mixed  with  the  plugs  belonging  to 
E  and  F.  Now  cause  the  acid  to  siphon  over,  drop  by  drop, 


102  QUANTITATIVE  CHEMICAL  ANALYSIS 

from  B  into  A  controlling  the  flow  by  holding  the  finger  against 
the  end  of  B  and  preventing  any  of  the  liberated  gas  from  escap- 
ing through  the  reservoir  tube.  When  all  of  the  acid  has  been 
drawn  into  A  and  when  the  decomposition  seems  to  be  complete, 
which  should  take  about  15  minutes  if  the  sample  has  been  finely 
ground,  heat  the  bulb  A  slowly  over  a  wire  gauze  until  the  solu- 
tion attains,  a  temperature  of  about  50°.  Next  connect  the  free 
ends  of  the  apparatus  with  the  tubes  E  and  F,  attach  the  latter  to 
an  aspirator,  and  draw  1500  cc.  of  air  thru  the  apparatus,  which 
should  require  about  20  minutes.  Disconnect  the  tubes  E  and  F 
and  replace  with  the  plugs  D  and  D'}  let  the  apparatus  stand  for  a 
half  hour  in  the  balance  room  and  weigh  as  before.  Report  the 
percentage  of  C02. 

IV.   QUESTIONS  AND  PROBLEMS.     SERIES  4 

1.  Assuming  that  the  capacity  of  the  Bunsen  apparatus  is  50  cc.,  that  the 
weight  of  a  liter  of  air  under  the  prevailing  conditions  is  1.2  gm.,  while  that 
of  carbon  dioxide  is  1.84  gm.,  how  large  a  departure  would  be  made  in  a 
determination  of  carbon  dioxide  in  2  gm.  of  pure  sodium  carbonate"_if  only  half 
the  carbon  dioxide  was  displaced  by  air  before  the  final  weighing  was  made? 

2.  What  other  determinations  might  be  made  with  a  Bunsen  apparatus? 

3.  Assuming  that  the  available  air  space  of  the  Bunsen  apparatus  was 
50  cc.  and  that  of  the  absorption  tube  was  10  cc.,  calculate  the  maximum 
and  minimum  volumes  of  air  which  should  be  passed  thru  the  apparatus  to 
reduce  the  carbon  dioxide  left  after  the  decomposition  to  1  mg.? 

4.  If  it  was  found  that  1  gm.  of  a  sample  consisting  of  a  mixture  of  sodium 
carbonate  and  sodium  bicarbonate  yielded  a  loss  of  0.46  gm.,  what  percentage 
of  Na2CO3  and  NaHCO3  must  have  been  present? 

Problems  of  this  kind  are  conveniently  solved  by  an  algebraic  method. 
Thus  if  x  represents  the  weight  of  Na-sCOs,  (1  —  x)  would  represent  the  weight 
of  NaHCO3  and  the  following  expression  is  then  true : 

-     mol.  wt.  CQ2  _  mol.  wt.  CO2 

'      V1 


mol.  wt.Na2  CO3  T  J  mol.  wt.  NaHCO3 

6.  If  an  error  of  0.2  mg.  was  made  in  making  the  determination  indicated 
in  the  last  problem,  how  large  an  error  would  appear  in  the  results  of  the 
calculation? 


CHAPTER  XIV 

DETERMINATION    OF    CARBON    DIOXIDE    IN    BAKING    POWDER 
BY    THE    ABSORPTION    METHOD 

I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Composition  of  the  Sample.  The  essential  constituents  of 
these  mixtures  are  starch,  bicarbonate  of  sodium,  and  some  reagent 
which  has  weakly  acidic  properties,  such  as  potassium  bitartrate, 
alum  or  the  acid  phosphate  of  calcium.  The  addition  of  water 
to  such  mixtures  brings  the  active  reagents  into  contact  with  each 
other  and  results  in  the  liberation  of  carbon  dioxide,  and  since  their 
efficiency  as  leavening  agents  depends  upon  the  volume  of  gas 
which  they  liberate  under  the  conditions  of  actual  usage,  the 
available  rather  than  the  total  carbon  dioxide  is  usually  deter- 
mined. The  weight  of  gas  liberated  when  the  sample  is  treated 
with  water  and  heated  can  be  determined  with  an  alkalimeter,  but 
the  equally  accurate  absorption  method,  which  has  been  more 
generally  used,  will  be  described  here.  The  starch,  which  is  added 
to  preserve  the  mixture,  does  not  affect  the  method  except  by  pro- 
ducing a  pasty  mass  when  heated  with  water. 

Properties  of  Soda  Lime.  The  substance  known  as  "  soda 
lime"  is  prepared  by  adding  calcium  oxide  to  a  strong  hot  solution 
of  sodium  hydroxide ;  on  cooling,  this  mixture  forms  a  solid  friable 
mass,  which  can  be  broken  into  pieces  and  packed  into  U-tubes. 
This  reagent  has  the  property  of  rapidly  absorbing  water  vapor, 
carbon  dioxide  and  other  gases  which  possess  acidic  properties, 
with  the  liberation  of  appreciable  amounts  of  heat.  Absorption 
of  carbon  dioxide  takes  place  most  rapidly  and  completely  if  the 
reagent  is  not  absolutely  dry.  As  the  lumps  of  reagent  used 

103 


104 


QUANTITATIVE  CHEMICAL  ANALYSIS 


rapidly  acquire  an  impervious  coating  of  calcium  carbonate,  which 
prevents  further  absorption  from  taking  place,  it  is  advisable  to 
pass  the  gas  thru  two  tubes  filled  with  the  reagent  and  to  deter- 
mine the  resulting  increase  in  the  weight  of  both.  Tubes  whose 
volume  does  not  exceed  25  cc.  are  more  efficient,  and  more  accu- 
rately weighed  than  those  of  greater  capacity.  A  tube  of  this  size 
when  properly  charged  should  weigh  about  25  gm.,  and  will  absorb 
at  least  1  gm.  of  carbon  dioxide. 


Fig.  24.  —  Plan  of  Apparatus  for  Determination  of  Carbon  Dioxide 

II.   CONSTRUCTION  OF  THE  APPARATUS 

Prepare  and  set  up  the  apparatus  represented  in  Fig.  24.  A  is 
the  decomposition  flask  of  about  125  cc.  capacity;  B  is  the  acid 
reservoir,  which  consists  of  a  separatory  funnel  of  about  40  cc. 
capacity;  C  is  a  condenser  of  the  Hopkins  form;  D  a  glass- 
stoppered  drying  tube  filled  with  calcium  chloride;  E  and  F 


CARBON  DIOXIDE  IN  BAKING  POWDER  105 

glass-stoppered  U  -tubes  of  about  25  cc.  capacity  filled  with  soda 
lime;  G  a  small  wash  bottle,  which  indicates  the  rate  at  which  air 
is  drawn  thru  the  apparatus;  H  an  aspirator  and  I  a  soda-lime 
tube  which  removes  the  carbon  dioxide  from  the  air  drawn  through 
the  apparatus.  The  stopper  of  the  flask  A  should  be  of  rubber, 
and  the  absorption  tubes  should  be  provided  with  wire  loops  by 
which  they  can  be  suspended  from  a  horizontal  support  when  in 
use,  and  from  the  balance  beam  when  being  weighed. 

III.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Preliminary  Operations.  Clean  the  parts,  A,  B  and  C,  by 
rinsing  with  acid  if  necessary,  then  with  water  and  allowing  them  to 
drain.  Clean  the  tubes  D,  E,  F  and  7  and  dry  by  wiping  them  as 
dry  as  possible  and  then  drying  in  an  oven.  Fill  the  tube  D  with 
lumps  of  calcium  chloride  not  exceeding  a  pea  in  size,  then  pass  dry 
carbon  dioxide  from  a  generator  thru  it  for  about  ten  minutes  and 
displace  the  latter  by  air.  In  like  manner  fill  the  tubes  E,  F  and 
7  with  soda  lime. 

Assemble  the  various  parts*  of  the  apparatus  and  test  for  leaks 
by  first  closing  the  free  end  of  the  tube  7  with  a  plug,  and  opening 
the  pinchcock  on  the  delivery  tube  of  the  aspirator;  if  water  con- 
tinues to  flow  from  the  aspirator  indefinitely,  test  each  joint  suc- 
cessively until  the  leak  is  found  and  stopped. 

Charging  the  Apparatus.  Disconnect  the  aspirator,  the  wash 
bottle  and  the  soda-lime  tubes  E  and  F  and  close  the  latter  by 
turning  the  stoppers.  Wipe  the  two  tubes  with  a  dry  cloth,  let 
them  stand  in  the  balance  room  for  a  half  hour  and  weigh  them  both 
separately,  using  a  glass  counterpoise.  Remove  the  flask  A  from 
the  apparatus,  wipe  it  dry  and  add  to  it  from  a  sample  tube  about 
2  gm.  of  the  sample,  being  careful  to  prevent  any  of  it  from  coming 
into  contact  with  the  side  of  the  flask,  then  again  weigh  the  sample 
tube.  Close  the  stopcock  of  the  separatory  funnel  and  charge 
the  latter  with  about  30  cc.  of  water.  Connect  the  reaction  flask 


106  QUANTITATIVE  CHEMICAL  ANALYSIS 

A,  the  soda-lime  tubes  E  and  F  and  the  wash  bottle  with  the 
rest  of  apparatus. 

Making  the  Decomposition.  Allow  the  water  to  run  into  the 
flask  A  by  cautiously  opening  the  stopcock  for  very  short  time 
intervals,  endeavoring  to  produce  a  slow  and  uniform  libera- 
tion of  the  gas.  After  all  of  the  water  has  been  introduced, 
attach  the  aspirator,  remove  the  plug  from  I  and  by  carefully 
regulating  the  aspirator  draw  a  slow  current  of  air  through  the 
apparatus.  Next  start  the  water  running  thru  the  condenser  and 
heat  the  solution  very  slowly  to  the  boiling  point,  then  allow  the 
flask  to  cool  very  slowly,  keeping  a  steady  stream  of  air  passing 
thru  the  apparatus. 

After  4  liters  of  air  have  been  passed  thru  the  apparatus,  which 
should  take  about  forty  minutes,  disconnect  the  two  soda-lime 
tubes  and  weigh  as  before.  Calculate  the  percentage  of  C02  from 
the  increase  in  the  weight  of  these  tubes. 

IV.   QUESTIONS  AND  PROBLEMS.     SERIES  5 

1.  Calculate  the  volume  of  COz  measured  at  25°  and  760  mm.  liberated  by 
1  gm.  of  a  sample  which  contains  12  per  cent  of  available  carbon  dioxide. 

2.  Assuming  that  air  contains  0.04  per  cent  by  volume  of  CO2  and  that 
-  2  liters  of  air  are  passed  thru  the  apparatus,  what  result  would  be  obtained  in 

this  determination  if  the  soda-lime  tube  I  was  not  used,  assuming  that  the 
correct  per  cent  of  CO2  is  12? 

3.  A  sample  of  baking  powder  which  is  known  to  contain  only  starch, 
NaHCO3   and   C4H5KOe    (potassium   bitartrate)    in   equivalent   proportions 
yields  12  per  cent  of  C02,  what  is  its  composition? 

4.  One  gram  of  a  mixture  consisting  of  CaCOs  and  PbCOs  is  found  to  con- 
tain 0.25  gm.  of  CO2.     What  percentages  of  CaO  and  PbO  must  be  present? 

5.  A  sample  which  contains  potassium  nitrate  is  analyzed  by  weighing  out 
1  gm.,  adding  3  gm.  of  sodium  paratungstate  (NaioWi2O4i)  and  heating  to  con-  . 
stant  weight  in  a  crucible.     If  the  crucible  shows  a  loss  of  0.3  gm.,  what  per- 
centage of  potassium  nitrate  was  present? 


CHAPTER  XV 

DETERMINATION   OF  MERCURY  IN  AN   ORE 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Decomposition  of  Mercuric  Sulfide.  The  ores  of  mercury 
which  are  of  commercial  importance  contain  the  element  as  the 
sulfide,  that  is,  the  minerals  cinnabar  or  metacinnabarate,  or  as 
metallic  mercury;  they  rarely  contain  more  than  a  small  per- 
centage. If  mixed  with  finely  divided  iron  filings  and  heated  the 
sulfide  is  decomposed  according  to  a  reaction  represented  by: 

HgS  +  Fe-*FeS  +  Hg. 

At  a  temperature  of  100°  metallic  mercury  gives  a  vapor  pressure 
of  0.27  mm.,  at  300°  the  pressure  is  242  xnm.;  hence  it  is  not  sur- 
prising to  find  that  this  reaction  can  be  made  complete  by  heat- 
ing the  mixture  to  a  temperature  of  300°  in  an  apparatus  one  part 
of  which  is  kept  at  a  temperature  which  does  not  exceed  100°,  that 
is,  by  condensing  the  vapor  as  it  is  formed. 

Condensation  of  Mercury  Vapor.  The  most  satisfactory  de- 
vice which  can  be  employed  for  the  retention  of  the  mercury  con- 
densed in  such  an  apparatus  takes  advantage  of  the  tenacity  with 
which  mercury  attaches  itself  to  plates  of  gold,  silver  or  copper, 
which  is  in  part  due  to  the  ease  with  which  it  forms  amalgams  with 
these  metals.  When  mercury  vapor  condenses  on  such  plates  it 
forms  a  thin  film  or  series  of  fine  drops,  and  although  they  can  be 
dislodged  by  brushing  or  vigorous  shaking  no  difficulty  is  ex- 
perienced in  accurately  determining  the  weights  of  mercury  ad- 
hering to  such  plates.  After  weighing,  the  mercury  can  be  expelled 

107 


108 


QUANTITATIVE  CHEMICAL  ANALYSIS 


o 


D 

= 

n 

^\ 

w 

'-J 

fj 

c  \  — 

B 

1 

by  heating  to  a  temperature  of  about  400°;  if  plates  of  gold  or 
silver  are  used  their  weights  remain  practically  constant;  if  a 
plate  of  copper  is  used  its  weight  increases  slightly,  owing  to 
oxidation. 

Form  of  Apparatus  Used.     Although  several  forms  of  appara- 
tus which  are  based  upon  the  facts  cited  have  been  suggested,  one 

devised  by  Whitton,*  which  is  repre- 
sented in  Fig.  25,  is  the  best.  It 
consists  of  an  iron  retort  A  of  24  cc. 
capacity,  a  sheet  of  silver  foil  B 
about  0.2  mm.  thick,  a  brass  dish  C 
which  is  kept  full  of  water,  an  iron 
shield  D  which  protects  the  foil  from 
the  flame  used  to  heat  the  retort,  and 
a  clamp  F  by  which  the  retort,  foil 
and  dish  are  held  together.  The 
silver  plate  used  is  about  5  cm. 
square,  and  weighs  about  2.3  gm.;  it 
can  be  used  for  twenty  or  more  de- 
terminations, but  after  repeated  use  seems  to  become  porous,  so 
that  some  of  the  mercury  may  pass  through  it. 

Sources  of  Error.  As  the  total  volume  of  air  expelled  from 
the  retort  during  the  heating  should  not  exceed  that  due  to  the 
expansion  of  the  air  originally  present,  and  the  maximum  con- 
centration of  this  air  with  respect  to  mercury  vapor  should  not 
exceed  that  of  air  saturated  at  100°  the  total  loss  from  this  source 
should  not  be  large. 

As  mercuric  sulfide  is  itself  appreciably  volatile,  a  relatively 
large  volume  of  iron  filings  should  be  used  to  insure  complete  de- 
composition. The  ore  and  filings  must  also  be  carefully  dried 
and  the  latter  washed  with  gasolene  or  ether  to  remove  any  grease 
with  which  they  may  be  contaminated.  The  maximum  amount 

*  Mineral  Industry,  17,  751  (1908).  Apparatus  can  be  procured  of  Braun- 
Knecht-Heinmann  of  San  Francisco. 


DETERMINATION   OF   MERCURY   IN  AN   ORE  109 

of  mercury  which  can  be  safely  retained  by  a  plate  of  the  size  given 
is  0.07  gm.,  and  the  amount  of  ore  used  for  the  determination  must 
be  chosen  with  this  statement  in  mind.  It  is  obvious  that  great 
care  should  be  used  in  weighing  the  foil. 

The  temperature  to  which  the  retort  is  heated,  and  the  length 
of  time  it  is  heated  in  order  to  insure  complete  decomposition, 
must  be  ascertained  by  experimenting  with  pure  mercuric  sulfide 
or  ores  of  known  composition.  When  the  flame  of  an  ordinary 
Bunsen  burner  is  used,  and  the  retort  is  so  placed  that  the  flame 
covers  the  bottom  and  reaches  a  point  one-half  inch  above  the 
bottom,  heating  for  20  minutes  is  found  to  give  good  results. 

An  entire  determination  can  be  made  within  an  hour  and  the 
method  is  peculiarly  adapted  to  the  analysis  of  low-grade  ores, 
since  a  large  amount  of  sample  can  be  used. 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Prepare  a  plate  of  silver  foil  by  polishing  with  a  piece  of  fine 
emery  or  crocus  cloth,  wiping  with  a  clean  cloth,  drying  for  a  few 
minutes  over  a  flame  and  weighing  with  the  greatest  attainable 
accuracy.  Weigh  out  about  5  gm.  of  iron  filings,  which  are  dry 
and  free  from  grease,  and  place  in  the  retort.  Weigh  out  on  a 
watch  glass  a  sufficient  amount  of  the  dry  ore  to  contain  from  20  to 
70  mg.,  and  transfer  to  the  retort.  Mix  the  ore  and  filings  very 
thoroughly  with  a  glass  rod,  and  cover  the  mixture  with  another 
gram  of  filings. 

Place  the  foil  between  the  retort  and  water  cooler,  clamp  all 
three  together  and  support  on  an  iron  ring  stand  above  a  burner 
so  that  the  top  of  the  burner  is  about  one  and  one-half  inches  below 
the  bottom  of  the  retort.  Fill  the  cooler  with  water,  light  the 
burner,  and  adjust  the  gas  supply  until  the  flame  runs  up  the 
sides  of  the  retort  for  not  more  than  one-half  an  inch,  which  should 
heat  the  water  to  boiling  in  7  minutes.  Renew  the  water  in  the 
dish  as  it  evaporates  and  after  20  minutes  remove  the  flame  and 
allow  to  cool  for  20  minutes,  then  disconnect  the  apparatus, 


110  QUANTITATIVE  CHEMICAL  ANALYSIS 

remove  the  plate  and  weigh  accurately.     Report  the  per  cent  of 
mercury. 

Expel  the  mercury  from  the  silver  plate  by  holding  it  with  the 
mercury-coated  side  uppermost,  several  inches  above  the  flame  of 
a  burner,  until  fumes  are  no  longer  given  off,  and  the  plate  shows  a 
faint  red  glow,  bub  avoid  using  a  temperature  which  \vould  melt  it. 


SECTION  III 
GRAVIMETRIC   PRECIPITATION   PROCESSES 


CHAPTER  XVI 

GENERAL  THEORY   OF  PRECIPITATION  PROCESSES 

Equilibrium  and  Solubility.  All  precipitation  processes  in- 
volve the  formation  of  a  new  solid  phase  from  a  liquid  phase,  and, 
therefore,  heterogeneous  equilibrium.  The  new  solid  phase  may 
result  from  the  addition  of  a  reagent  which  changes  the  physical 
properties  of  the  solvent  and  reduces  the  solubility  of  the  con- 
stituent which  separates,  or  from  a  chemical  reaction  brought 
about  by  the  addition  of  a  reagent,  or  from  the  action  of  a  galvanic 
current.  Since  the  concentration  of  the  substance  precipitated,  in 
the  solution  from  which  it  separates,  cannot  exceed  that  of  a  satu- 
rated solution  of  this  precipitate,  equilibrium  in  those  reactions 
which  result  in  the  formation  of  precipitates  is  determined  by  the 
solubility  of  the  precipitate.  The  solubility  at  ordinary  temper- 
atures, expressed  in  milligrams  per  liter  of  solution,  of  some  of 
the  precipitates  frequently  used  in  quantitative  analysis  is  given 
in  the  following  table.* 


AgCL. 

2.0  **# 

Ca(COO)2.. 

5  6 

AgBr       .... 

0  13    ' 

CaSO4 

2004  0 

Agl  

0.0025 

Cul  

0  43 

AgCNS  

0.02 

PbSO4.. 

44  0 

Ag2CrO4  

25  0 

PbCrO4  . 

0  2 

Ag2O 

25  0 

SrSO4 

100  0 

BaCO3  

18  6 

Sr(COO)2 

46  0 

BaSO4  

2.3 

*  Most  of  the  figures  given  here  have  been  calculated  from  the  data  sum- 
marized in  the  Landolt-Bornstein,  Physikalische-Chemische  Tabellen. 

Ill 


112  QUANTITATIVE   CHEMICAL   ANALYSIS 

The  Solubility  of  Electrolytes.  Let  us  represent  the  total 
solubility  of  a  binary  electrolyte,  such  as  silver  chloride,  expressed 
in  moles  per  liter  by  m  and  its  degree  of  dissociation  in  this  solution 
by  x.  Then  mx  represents  the  concentration  of  the  dissociated 
electrolyte  and  also  that  of  the  anion  and  cation;  also  m  (1  —  x) 
represents  the  concentration  of  the  undissociated  electrolyte.  If 
the  dissociation  of  the  electrolyte  obeys  the  mass  law  the  relation 
between  the  concentrations  is  expressed  by  the  equation 

(mx)'1  —  k  •  m  (1  —  x). 

In  the  solution  under  consideration  both  m  (1  —  x)  and  (mx)z  are 
constant  and  since  both  bear  a  simple  relation  to  the  total  solu- 
bility either  could  be  used  as  a  measure  of  the  total  solubility. 
The  value  of  (mx)2  has  been  largely  used  in  expressing  the  solu- 
bility of  electrolytes,  it  has  been  designated  by  Ostwald  as  the 
"solubility  product."  The  solubility  of  those  electrolytes  which 
are  of  importance  in  quantitative  analysis  is  so  small  that  their 
dissociation  can  be  considered  complete,  and  the  solubility  product 
of  all  such  binary  electrolytes  is  their  total  solubility  expressed  in 
moles  per  liter  raised  to  the  second  power. 

When  a  precipitate  results  from  a  chemical  reaction,  an  excess 
of  the  reagent  used  is  invariably  added,  and  the  concentration 
of  either  anion  or  cation  which  enters  into  the  formation  of  the 
precipitate  must  exceed  the  concentration  of  the  anion  or  cation 
in  a  solution  of  the  precipitate  which  contains  no  other  substances. 
In  discussing  the  effect  of  other  substances  upon  the  solubility  of 
such  electrolytes  it  was  assumed  by  Nernst  that  "In  any  saturated 
solution  of  a  slightly  soluble  electrolyte  the  concentration  of  the 
undissociated  electrolyte,  and  also  the  product  of  the  concentra- 
tions of  the  ions  into  which  it  dissociates,  are  constant."  These 
theorems  merely  assert  that  the  values  which  represent  the  con- 
centrations of  the  undissociated  electrolyte  and  the  solubility 
product  in  solutions  obtained  by  saturating  water  with  the  pure 
electrolyte  are  true  for  all  solutions  of  that  electrolyte,  that  is, 


GENERAL  THEORY  OF  PRECIPITATION  PROCESSES      113 


are  not  affected  by  the  presence  of  other  substances.  If  they  are 
true  the  addition  of  an  excess  of  the  precipitating  agent  must 
decrease  the  solubility  of  the  precipitate.  ^ 

Theory  of  the  Precipitation  of  Silver  Chloride.  Let  us  assume 
that  we  precipitate  the  chlorine  in  200  cc.  of  a  0.2  molar  solution 
of  sodium  chloride  by  the  addition  of  silver  nitrate  in  solid  form, 
in  order  to  avoid  changing  the  dilution.  If  we  first  add  an  exactly 
equivalent  amount,  that  is,  0.04  mole  of  the  silver  salt,  the  ratio 
of  the  silver  salt  added  to  salt  present  is  1,  and  the  mixture  must 
contain  equal  concentrations  of  Ag  and  Cl  ions.  One  liter  of  water 
saturated  with  AgCl  contains  0.002  gm.,  and  the  concentration 
of  the  solution  in  moles  is  0.002  -f-  143  =  1.38  X  10~5.  This  also 

Log  of  Solubility  of  AgCl 


-6 


-7 


V 


8 


1.01  1.02  1.03 

Ratio  of  Silver  Added  to  Chlorine  Present  '< 


Fig.  26.  — Changes  in  the  Solubility  of  Silver  Chloride 

represents  (Ag+)  and  (Cl~)  and  its  square,  that  is,  1.9  X  10~10,  the 
solubility  product. 

Let  us  now  increase  (Ag+)  to  0.001  by  the  addition  of  0.0002 
mole  of  the  silver  salt,  which  will  change  the  ratio  of  silver  added 
to  salt  present  to  1.005.  If  we  assume  that  both  sodium  chloride 
and  silver  nitrate  are  completely  dissociated  this  addition  must 
change  (Cl~)  to  1.9  X  10-10  -f-  0.001,  or  1.9  X  10~7,  that  is,  a  very 
slight  increase  in  the  amount  of  reagent  used  reduces  the  solubility 
of  the  precipitate  enormously.  The  relation  between  solubility 
and  amount  of  reagent  used  is  shown  in  the  curve  represented  in 
Fig.  26,  in  which  the  abscissas  represent  the  ratios  of  silver  salt  to 


114  QUANTITATIVE  CHEMICAL  ANALYSIS 

sodium  chloride,  and  the  ordinates  the  logarithm  of  the  solubility. 
It  is  important  to  note  that  the  rate  at  which  the  solubility  is 
reduced  decreases  very  rapidly  as  the  value  of  the  ratio  increases 
from  1.  It  is  also  evident  that  if  sodium  chloride  is  used  for  the 
precipitation  of  silver  from  a  silver  salt,  exactly  the  same  reduction 
in  solubility  must  be  effected  by  the  addition  of  an  amount  of 
sodium  chloride  which  makes  the  ratio  of  sodium  chloride  to  silver 
salt  the  same  as  the  ratio  of  silver  salt  to  sodium  chloride  at  the 
points  represented  on  the  curve.  The  precipitate  has  a  maximum 
solubility  when  this  ratio  has  the  value  1. 

Factors  Which  Affect  the  Theory.  Ideal  conditions  have  been 
assumed  in  the  preceding  paragraph.  The  dissociation  of  both 
precipitate  and  added  salt  has  been  assumed  to  be  complete,  and 
the  formation  of  complex  ions  has  been  entirely  disregarded.  In 
attempting  to  test  'the  theory  by  comparing  calculated  with 
observed  changes  in  solubility  it  is  scarcely  possible  to  maintain 
such  conditions.  The  solubility  of  most  of  the  precipitates  tabu- 
lated on  page  111  is  so  small  that  the  experimental  error  involved 
in  determining  the  change  in  solubility  resulting  from  the  addition 
of  a  slight  amount  of  the  added  salt  is  large.  Hence  in  most  of 
the  investigations  made,  either  relatively  soluble  precipitates  have 
been  used,  or  the  concentration  of  the  added  salt  has  been  made 
large.  In  the  former  case  the  dissociation  of  the  precipitate,  and 
in  the  latter  case  the  dissociation  of  the  added  salt  cannot  be 
considered  complete,  and  it  becomes  necessary  to  ascertain  and 
make  use  of  the  degree  of  dissociation  of  the  electrolytes  in  cal- 
culating the  change  in  solubility  concerned.  These  values  cannot 
be  determined  by  a  direct  measurement  in  solutions  which  contain 
more  than  one  electrolyte,  and  all  attempts  to  calculate  them 
from  the  experimental  data  involve  assumptions  whose  validity 
can  be  questioned.  In  spite  of  these  difficulties  many  results 
have  been  obtained  which  agree  fairly  well  with  the  predictions 
of  the  theory,  others  show  wide  variations  from  them. 

In  some  cases  also  the  formation  of  complex  ions  may  render 


GENERAL  THEORY  OF  PRECIPITATION   PROCESSES      115 

the  results  of  such  calculations  valueless.  It  seems  necessary  to 
assume  that  all  ions,  especially  those  which  possess  a  slight  degree 
of  affinity  for  their  charges,  show  a  variable  tendency  to  increase 
this  affinity  by  taking  up  undissociated  molecules  from  the  solu- 
tion. The  large  number  of  double  salts  which  can  be  prepared, 
and  which  can  be  assumed  to  result  from  the  combination  of  such 
ions  with  others  of  opposite  sign,  support  this  statement.  This 
tendency  for  the  formation  of  complex  ions  increases  with  the 
concentration  of  the  electrolyte  taken  up;  it  is  responsible  for  two 
effects  which  are  of  importance  in  quantitative  analysis.  In  some 
cases  it  leads  to  the  formation  of  precipitates  of  abnormal  com- 
position, as  shown  in  the  chapter  on  occlusion;  in  others  it  increases 
the  solubility  of  a  precipitate  thru  the  formation  of  complex  ions, 
which  makes  it  possible  for  the  solution  to  attain  a  higher  concen- 
tration of  the  constituent  which  is  being  separated  than  would  be 
possible  if  the  simpler  ions  only  were  present. 

For  example,  it  was  found  that  the  solubility  of  silver  choride* 
in  a  solution  containing  0.933  mole  of  sodium  chloride  per  liter 
was  8.6  X  10~4,  that  is,  nearly  sixty  times  as  great  as  its  solubility 
in  pure  water. 

Results  of  this  character  have  lead  some  chemists  f  to  the 
conclusion  that  one  or  both  of  the  fundamental  assumptions  made 
by  Nernst  must  be  rejected;  others  believe  that  the  results  of  the 
calculations  based  upon  them  are  limiting  values  toward  which 
the  actual  values  converge  in  proportion  as  the  actual  conditions 
approach,  ideal  conditions. 

Theory  of  Separation  of  Two  Closely  Related  Ions.  The  pos- 
sibility of  separating  two  ions  by  the  addition  of  a  reagent  which 
is  capable  of  forming  slightly  soluble  compounds  with  both  can 
be  discussed  with  advantage  from  the  standpoint  of  the  theory 
already  elaborated.  Let  it  be  assumed  that  silver  nitrate  is 
slowly  added  to  a  solution  containing  equivalent  concentrations 

*  Hill,  Jour,  of  Amer.  Chem.  Soc.,  32,  1186  (1910.) 

t  Arrhenius,  Zeit.  fur  physikalische  Chemie,  31,  224  (1899). 


116  QUANTITATIVE  CHEMICAL  ANALYSIS 

of  potassium  iodide  and  potassium  chloride.  Silver  iodide  must 
begin  to  separate  as  soon  as  the  product  (Ag+)  X  (I~)  exceeds  S, 
where  S  represents  the  solubility  product  of  silver  iodide,  and  silver 
chloride  must  begin  to  separate  as  soon  as  the  product  (Ag+)  X 
(Cl~)  exceeds  AS',  where  S'  represents  the  solubility  product  of  silver 
chloride.  As  more  silver  nitrate  is  added,  more  silver  iodide 
separates,  and  (I~)  is  progressively  reduced.  Since,  further,  the 
solution  remains  saturated  with  respect  to  silver  iodide,  and  S  is 
constant,  the  concentration  of  the  silver  ions  must  progressively 
increase.  Both  of  these  changes  will  continue  until  (Ag+)  has 
become  so  large  that  the  solution  is  also  saturated  with  respect  to 
silver  chloride.  At  this  point 

(Ag+)  X  (C1-)  =  S,    and     (Ag+)  X  (C1-)  =  S'. 

Since  both  these  expressions  relate  to  the  same  solution  (Ag+) 
has  the  same  value  in  both,  and  hence 

(I)-    _  S 


(Cl)-     S' 

This  expression  tells  us  that  the  condition  for  saturation  with 
respect  to  both  compounds  is  that  (I~)  shall  bear  the  same  relation 
to  (Cl~)  that  S  bears  to  S'.  If  still  more  silver  nitrate  is  added 
further  quantities  of  both  silver  iodide  and  silver  chloride  must 
separate,  but  the  relation  of  (I~)  to  (Cl~)  must  remain  constant. 
The  solubility  product  of  silver  iodide  can  be  calculated  from  the 
data  given  on  page  111  to  be  1  X  10~16,  and  that  of  silver  chloride 
to  be  1.9  X  10~10.  Therefore  the  condition  for  saturation  with 
both  salts  is 

(I-)         1  X  IP"16    =  5.3  X  1Q-7 

(C1-)      1.9  X  10-10  1 

That  is,  the  concentration  of  the  iodide  ions  must  be  reduced  to 
5.3  X  10~7  X  Cl~  before  precipitation  of  the  chlorine  ions  can  begin 
to  take  place. 


GENERAL  THEORY  OF  PRECIPITATION   PROCESSES      117 

If,  further,  it  is  assumed  that  one  equivalent  of  silver  is  added 
for  every  equivalent  of  iodine  present,  the  concentration  of  both 
iodine  and  silver  would  be  Vl  X  10~16,  or  IX  10~~8,  and  hence 
the  maximum  concentration  of  chlorine  ions  which  could  be 
present  without  causing  some  silver  chloride  to  separate  would  be 
(1  X  10-8)  -f-  (5.3  X  10~7),  or  0.019;  that  is,  if  the  concentration 
of  Cl  reached  the  value  0.019  and  if  one  equivalent  of  silver  was 
added  for  every  equivalent  of  iodine  present,  the  solution  would 
be  just  saturated  with  both  precipitates.  It  is  clear  that  an 
accurate  separation  of  the  iodine  from  solution  which  contains 
both  iodine  and  chlorine  ions  would  not  be  possible  except  within 
certain  narrow  limits.  Obviously  one  equivalent  of  silver  would 
have  to  be  added  for  every  equivalent  of  iodine  present  if  all  the 
latter  was  to  be  entirely  precipitated,  but  even  if  no  excess  were 
used  some  silver  chloride  would  separate  if  the  concentration  of 
the  chlorine  ion  exceeded  0.019. 

The  separation  of  two  ions  which  yield  precipitates  with  the 
same  reagent  is  scarcely  possible  unless  the  solubilities  of  these 
precipitates  differ  by  large  amounts,  and  even  then  the  amount 
of  reagent  used  must  be  properly  adjusted  to  the  concentrations  of 
the  two  ions  present. 


CHAPTER  XVII 

FILTERING,   WASHING  AND   IGNITING   PRECIPITATES 

Media  Used  for  Filtration.  The  separation  of  precipitates 
from  liquids  is  essentially  a  process  of  straining,  in  which  solid 
particles  are  separated  from  liquid  particles  by  the  use  of  a  porous 
diaphragm.  A  variety  of  media  which  differ  greatly  as  to  their 
efficiency  and  adaptability  to  different  purposes  are  employed  for 
such  separations. 

Cellulose  made  into  the  form  of  paper  of  a  loose,  open  texture  has 
many  advantages;  it  should  represent  the  purest  possible  form  of 
this  substance,  and  is,  therefore,  digested  with  both  hydrochloric 
and  hydrofluoric  acids  and  washed  very  carefully  before  use,  for 
the  purpose  of  reducing  the  percentage  of  inorganic  salts  present 
to  a  minimum.  It  is  not  appreciably  dissolved  or  otherwise 
affected  by  solutions  of  salts  or  by  acids  and  bases  of  moderate 
concentration,  but  is  attacked  by  strong  solutions  of  acids  and 
bases,  and  cannot  be  used  for  the  filtration  of  -such  solutions. 
The  papers  made  from  it  for  quantitative  separations  differ  greatly 
as  to  thickness  and  texture;  those  of  an  open  and  porous  character 
permit  very  rapid  filtration,  but  are  unable  to  retain  very  fine 
precipitates;  the  more  compact  varieties  are  more  efficient  but 
slower. 

Asbestos  or  mineral  wool,  unlike  cellulose,  is  non-combustible; 
it  should  not  be  appreciably  hygroscopic.  Different  grades  of  the 
mineral  vary  greatly  as  to  their  freedom  from  associated  minerals, 
length  of  fiber,  and  the  ease  with  which  they  can  be  reduced  to  a 
satisfactory  pulp.  The  best  is  the  pure  white  long-fibered  variety, 
which  can  be  easily  reduced  to  a  pulpy  mass  by  triturating  with 

118 


FILTERING,   WASHING  AND   IGNITING  PRECIPITATES      119 

water  in  an  agate  mortar.  It  is  customary  to  digest  with  strong 
hydrochloric  acid  before  use  in  order  to  remove  any  impurities 
present  which  might  be  dissolved  during  its  use  as  a  filter  and 
thereby  change  its  weight,  or  contaminate  the  resulting  nitrate. 
It  is  not  readily  made  into  a  fabric  which  can  be  used  like  paper, 
but  must  be  supported  on  a  plate  or  disk  of  platinum  or  porcelain, 
which  is  provided  with  a  number  of  fine  holes  (Witt  filter  plates), 
or  on  a  crucible  the  bottom  of  which  is  similarly  provided. 

Glass  wool  is  used  in  the  same  manner  as  asbestos.  As  the 
fibers  of  which  it  is  composed  are  more  elastic  and  pack  together 
less  compactly  than  asbestos  it  is  not  so  readily  made  into  a  filter 
of  equal  efficiency. 

Platinum  sponge,  which  is  easily  made  by  reducing  the  salts  of 
that  element  to  the  metallic  state,  is  also  used  like  asbestos  but 
is  too  expensive  for  any  but  certain  special  purposes. 

Alundum,  or  fused  aluminum  oxide,  which  has  been  crushed  to 
a  fine  powder,  can  also  be  made  into  an  efficient  filter.  It  is  usually 
mixed  with  a  small  amount  of  cementing  material  and  molded 
into  the  form  of  crucibles  or  cylinders.  It  is  not  appreciably 
affected  by  treatment  with  even  strong  acids  or  strong  alkalies. 

Devices  for  Filtering  When  the  Precipitate  Is  Not  To  Be 
Weighed.  In  discussing  the  devices  used  in  filtration  we  can  dis- 
tinguish between  those  cases  in  which  the  precipitate  is  to  be 
weighed  at  once,  and  those  in  which  the  separation  is  only  one  of 
the  preliminary  operations  which  precede  the  final  separation  of 
the  desired  substance.  In  the  latter  case  the  precipitate  may  be 
discarded  entirely,  or  it  may  be  again  brought  into  solution  by 
treatment  with  other  reagents,  and  the  desired  substance  can  be 
separated  from  the  resulting  solution  by  farther  operations.  Two 
classes  of  devices  are  usually  employed  in  such  cases.  The  first 
and  simplest  consists  of  a  paper  filter  supported  on  a  glass  funnel. 
The  rate  at  which  a  liquid  passes  thru  such  a  device  depends, 
aside  from  the  character  of  the  filter  paper,  upon  the  nature 
of  the  precipitate  and  the  viscosity  of  the  liquid  filtered.  It 


120 


QUANTITATIVE  CHEMICAL  ANALYSIS 


g> 


can  be  greatly  increased  by  lengthening  the  funnel  stem,  that 
is,  by  attaching  to  the  latter  a  piece  of  glass  tubing,  which  is 
bent  to  form  a  complete  turn  near  its  upper  end  and  is  slightly 
constricted  at  its  lower  end  as  represented  in  Fig.  27.  If  the  paper 
is  accurately  fitted  to  the  funnel  and  the  outlet  of  the  stem  is  small 
enough  to  prevent  air  from  entering,  the  tube 
gradually  fills  with  liquid  and 
ST  ~7  the  pressure  exerted  by  the 

liquid  assists  in  drawing  fur- 
ther quantities  of  it  thru  the 
filter.  If  the  tube  is  made 
too  long  the  pressure  may  be 
great  enough  to  break  the 
paper  at  the  apex  of  the  fun- 
nel as  it  is  unsupported  at 
that  point;  hence  it  is  often 
necessary  to  introduce  a  sup- 
port in  the  form  of  a  cone 
made  of  very  thin  platinum 
foil  and  provided  with  a  num- 
ber of  fine  openings  or  of  a 
small  piece  of  linen  cloth 
folded  to  fit  the  apex  of  the 
funnel. 

Whenever  a  paper  filter  is  used  some  of  the  precipitate,  especially 
if  the  latter  is  finely  divided,  is  carried  into  the  interior  of  the 
paper,  and  when  it  is  desired  to  bring  this  precipitate  into  solution 
or  to  treat  it  with  other  reagents  a  large  volume  of  reagent  must 
be  poured  thru  it,  or  the  entire  filter  must  be  opened  out  and 
digested  in  a  separate  vessel.  This  often  consumes  much  time, 
requires  the  use  of  an  undesirably  large  volume  of  reagent  and 
increases  the  total  volume  of  the  solution  to  an  undesirable  amount; 
also  the  cellulose  of  the  filter  may  be  attacked  by  the  reagent 
which  it  is  desired  to  use. 


Fig.  27.  — Fun- 
nel for  Rapid 
Filtration 


Fig.  28.  —  Filtering 
Tube  and  Suction 
Flask 


FILTERING,  WASHING  AND  IGNITING  PRECIPITATES      121 

These  difficulties  are  all  avoided  by  the  use  of  an  asbestos  filter 
such  as  is  shown  in  Fig.  28,  in  which  a  Witt  filter  plate  is  used  in 
the  bottom  of  a  " filtering  tube."  In  this  and  all  devices  in  which 
asbestos  pulp  is  used,  suction  greater  than  that  easily  obtained  by 
increasing  the  length  of  the  stem  of  the  funnel  is  necessary.  In 
the  device  shown  in  the  figure  the  filter  tube  is  attached  to  a  closed 
filter  flask  by  means  of  a  rubber  stopper,  and  the  flask  is  attached 
thru  its  side  neck  to  a  Bunsen  pump  or  some  other  suction  device. 
It  permits  of  extremely  rapid  filtration  and  by  varying  the  thick- 
ness and  fineness  of  the  asbestos  layer,  precipitates  of  any  desired 
fineness  can  be  retained.  After  the  filtration  has  been  completed 
the  filter  and  adhering  precipitate  can  be  readily  and  completely 
transferred  to  another  vessel,  and  treated  with  any  desired  reagent, 
even  with  strong  bases  or  acids,  after  which  the  residual  asbestos 
can  be  removed  by  a  second  filtration. 

Devices  for  Filtration  When  the  Precipitate  Is  To  Be  Weighed. 
If  the  precipitate  is  to  be  weighed  it  must  be  freed  from  water  and 
other  adhering  substances,  and  often  must  be  strongly  ignited 
before  it  can  be  accurately  weighed.  It  is  extremely  desirable, 
therefore,  that  the  medium  used  for  the  filtration  shall  have  such 
properties,  that  it  can  be  treated  exactly  as  the  precipitate  is 
treated  without  danger  of  affecting  changes  in  its  weight,  and  that 
the  filter  used  shall  be  of  such  a  form  that  it  can  be  easily  ignited 
and  accurately  weighed  both  before  use,  and  after  the  precipitate 
has  been  separated  on  it. 

Cellulose  is  decidedly  hygroscopic  and  furthermore  slowly  loses 
water  and  carbonizes  even  at  a  temperature  of  100°,  and  altho  it  is 
sometimes  considered  necessary  to  weigh  a  precipitate  on  a  paper 
filter  it  should  be  avoided  wherever  possible.  When  this  medium 
is  used  for  filtration  it  is  customary  to  destroy  the  entire  filter  by 
burning  in  a  good  supply  of  air  and  to  weigh  the  residual  precipitate 
mixed  with  the  ash  of  the  paper  in  a  crucible.  As  the  ash  content 
of  the  filter  should  not  exceed  .1  mg.  it  can  usually  be  disregarded. 

Asbestos,  glass  wool  and  platinum  sponge  can  be  ignited  strongly 


122 


QUANTITATIVE  CHEMICAL  ANALYSIS 


without  suffering  appreciable  changes  in  weight,  and  are,  therefore, 
to  be  preferred  to  paper  in  such  cases.  The  most  convenient 
form  for  a  filtering  device  in  which  such  media  are  to  be  used  and 
the  precipitate  is  to  be  ignited,  is  that  of  a  crucible  of  tall  form  but 
of  moderate  size  and  weight  such  as  is  represented  in  Fig.  29. 
This  is  the  device  first  used  by 
Gooch  and  is  usually  known  as  a 
Gooch  crucible.  Its  bottom  is 
pierced  by  a  number  of  fine  holes 
and  furnishes  a  support  for  the 
media  named.  It  is  connected  with 
a  filtering  tube  by  means  of  a 
rubber  band  and  this  tube  is  at- 
tached to  a  filter  flask  as  shown  in 
the  figure. 

A  crucible  of  alundum  is  equally 
satisfactory,  but  since  the  entire  cru- 


\ 


Fig.  29 .—  Gooch  cible  is  made    of   porous  material  Fig.  30.  — Glass 


Crucible 


Filtering  Tube 


more  time  and  care  must  be  ex- 
pended in  washing  the  filter  free  from  soluble  salts  than  where 
the  bottom  layer  only  constitutes  the  filtering  medium. 

When  it  is  not  necessary  to  heat  the  precipitate  after  filtration 
to  more  than  350°  a  glass  filter  tube,  similar  to  the  one  represented 
in  Fig.  30,  which  is  used  in  conjunction  with  a  Witt  plate  or 
platinum  cone  can  be  used  to  advantage. 

The  Different  Classes  of  Precipitates.  All  substances  which 
have  been  separated  as  precipitates  possess  certain  physical 
peculiarities,  altho  these  peculiarities  may  be  modified  to  some 
extent  by  varying  the  conditions  of  precipitation.  They  may  be 
roughly  classified  as  follows: 

Crystalline  precipitates,  such  as  calcium  sulfate,  calcium  oxalate 
and  magnesium  ammonium  phosphate.  They  frequently  contain 
water  of  crystallization  and  possess  a  definite  crystalline  form, 
which  can  be  recognized  by  a  magnification  of  about  three  hundred 


FILTERING,   WASHING  AND   IGNITING  PRECIPITATES      123 

diameters.  In  this  type  the  tendency  for  the  formation  of  super- 
saturated solutions,  from  which  the  normal  amount  of  precipitate 
separates  but  slowly,  is  most  pronounced,  and  often  makes  it  de- 
sirable to  make  use  of  mechanical  shaking  devices  when  it  is  nec- 
essary to  reduce  the  time  needed  for  the  complete  separation  of 
the  precipitate  to  a  minimum.  The  solubility  of  these  precipitates 
is  comparatively  large,  and  the  addition  of  special  reagents  for  the 
reduction  of  the  error  from  solubility  often  becomes  necessary. 
They  are,  however,  extremely  easy  to  filter  and  wash. 

Pulverulent  precipitates,  such  as  the  sulfates  of  lead  and  barium, 
and  the  phosphomolybdate  of  ammonium,  are  composed  of 
spherical  or  indefinitely  bounded  particles,  which  are  too  small 
to  be  recognized  as  individuals  except  by  very  high  magnification. 
The  particles  are  sometimes  so  fine  that  it  is  difficult  to  retain  them 
on  paper  filters,  unless  these  are  very  hard  and  dense.  It  is  often 
possible  to  avoid  the  formation  of  such  particles  by  using  condi- 
tions which  make  the  precipitate  separate  very  slowly,  that  is,  by 
diluting  both  the  original  solution  and  the  added  reagent,  and  by 
adding  the  latter  slowly  and  with  constant  stirring.  Long-con- 
tinued digestion  also,  will  frequently  increase  the  size  of  the  smaller 
grains  as  explained  on  page  33.  Some  precipitates  of  this  class 
are  more  satisfactory  if  separated  from  a  hot,  others  from  a  cold 
solution,  and  the  best  conditions  of  treatment  for  every  precipitate 
must  be  learned  thru  experiment. 

Another  peculiarity  of  such  precipitates  is  their  tendency  to 
"  creep, "  that  is,  small  amounts  of  the  very  fine  particles  are  carried 
thru  capillary  action  over  the  sides  of  the  filter  and  above  the 
liquid  which  it  contains,  and  where  a  paper  filter  is  used  appreciable 
amounts  may  be  carried  entirely  out  of  the  filter  and  on  to  the  sides 
of  the  funnel.  The  method  of  treatment  adopted,  and  the  pres- 
ence of  certain  reagents  seems  to  have  some  effect  on  this  pecu- 
liarity. 

Curdy  precipitates  are  very  similar  to  those  classed  as  pulveru- 
lent but  are  peculiar  in  that  the  very  fine  particles  of  which  they 


124  QUANTITATIVE  CHEMICAL  ANALYSIS 

are  composed  readily  coalesce  to  form  curdy  masses.  This  is  often 
spoken  of  as  " coagulation"  and  can  be  assisted  by  heating,  violent 
stirring,  and  by  the  presence  of  certain  reagents.  This  class  of 
precipitates  is  one  of  the  most  desirable,  as  they  are  easily  and 
rapidly  filtered  and  washed.  The  chloride,  iodide  and  cyanide  of 
silver  and  the  sulphocyanide  of  copper  are  good  examples. 

Flocculent  precipitates  are  entirely  amorphous  and  very  bulky. 
They  are  made  up  of  large  aggregates  of  fine  particles,  which  are 
normally  of  a  loose  flocculent  nature,  but  may  become  hard  and 
compact  if  allowed  to  dry,  or  if  sucked  against  the  bottom  of  the 
filter  by  pressure.  Under  some  conditions,  they  become  slimy 
or  gelatinous,  and  are  then  extremely  difficult  to  filter.  They  are 
usually  separated  in  the  best  conditions  for  filtration  if  the  solution 
is  hot,  but  long-continued  boiling  sometimes  makes  them  slimy. 
They  retain  soluble  salts  readily  and  are  hard  to  wash  completely. 
Ferric  hydroxide  furnishes  a  typical  illustration. 

Gelatinous  precipitates,  such  as  the  hydroxide  of  aluminum,  are 
also  composed  of  extremely  fine  particles  which  tend  to  aggregate 
into  jelly-like  masses.  They  are  extremely  bulky  and  as  they 
rapidly  clog  up  the  pores  of  the  filter  are  very  hard  to  filter  and 
wash.  In  general,  they  are  best  kept  off  the  filter  until  nearly  all 
of  the  liquid  present  has  been  passed  thru  it. 

Colloidal  precipitates  are  distinguished  by  their  tendency  to 
form  "pseudosolutions"  and  the  best  examples  are  found  in  the 
sulfides  of  the  copper  and  arsenic  group  and  silicic  acid.  When 
treated  with  water  these  solids  undergo  a  transformation  which 
results  in  the  formation  of  a  mixture  that  seems  to  be  a  homo- 
geneous solution  and  readily  passes  thru  a  filter,  even  tho  the 
latter  is  capable  of  retaining  extremely  fine  particles.  Such 
mixtures  are  not  homogeneous,  for  it  can  be  shown  by  the  use  of 
the  ultramicroscope  that  they  actually  contain  solid  particles  of 
too  small  a  size  to  be  recognized  by  the  usual  methods  of  mag- 
nification. The  formation  of  such  pseudosolutions  can  be  entirely 
prevented  by  keeping  a  small  concentration  of  some  electrolyte 


FILTERING,  WASHING  AND  IGNITING  PRECIPITATES      125 

in  the  liquid  with  which  they  are  in  contact.  As  most  precipitates 
are  formed  in  the  presence  of  one  or  more  electrolytes  no  difficulty 
is  usually  experienced  in  filtering  them,  but  when  they  are  washed 
with  pure  water  pseudosolutions  may  form  as  soon  as  the  con- 
centration of  the  electrolyte  has  been  sufficiently  reduced;  the 
solid  which  passes  thru  the  filter  in  this  form  is  usually  reprecipi- 
tated  on  coming  into  contact  with  the  main  filtrate. 

It  becomes  necessary,  therefore,  to  wash  such  precipitates  with 
a  solution  of  some  electrolyte.  Electrolytes  differ  greatly  in  their 
ability  to  prevent  the  formation  of  pseudosolutions  and  altho 
the  salts  of  di-  or  tri-valent  metals  are  much  more  efficient  than 
the  salts  of  ammonium  the  latter  are  very  generally  used  for  this 
purpose,  as  they  can  be  entirely  volatilized  by  igniting  the  pre- 
cipitate. 

The  Theory  of  Washing  Precipitates.  The  precipitate  finally 
separated  on  the  filter  is  contaminated  with  various  soluble 
substances  present  in  the  solution  associated  with  it.  If  these 
substances  are  easily  volatilized  during  the  subsequent  ignition, 
and  if  they  do  not  react  with  the  precipitate  in  such  a  manner  as 
to  give  rise  to  volatile  compounds  with  the  precipitate  during  the 
ignition,  their  removal  is  not  necessary.  In  the  great  majority 
of  cases  both  of  these  conditions  are  not  complied  with  and  the 
precipitate  must  be  washed  with  an  appropriate  liquid,  the  amount 
of  which  should  be  made  as  small  as  possible,  owing  to  the  solvent 
action  of  the  liquid  on  the  precipitate. 

The  efficiency  of  the  method  used  in  washing  precipitates  is 
readily  calculated  if  ideal  conditions  only  are  considered.  If  A 
represents  the  weight  in  grams  of  the  impurity  to  be  removed 
and  V  the  volume  in  cubic  centimeters  of  the  wash  solution  added, 
and  if  it  is  assumed  that  the  filter  is  in  all  cases  allowed  to  drain 
until  only  1  cc.  of  liquid  remains  in  contact  with  it,  and  that  there 
is  an  equal  distribution  of  the  soluble  salt  thruout  the  volume  of 

V 

liquid  used,  each  washing  would  remove   /y  ,   *\  A  gm.  of  the 


126  QUANTITATIVE  CHEMICAL  ANALYSIS 

impurity  and  leave   ,v  .   -.N  A  gm.  behind.     The  general  expres- 
sion for  the  amount  of  impurity  left  on  the  filter  after  n  treatments 


is  f  v  _     }  A.     If,  for  example,  the  amount  of  impurity  to  be 

removed  was  0.2  gm.  and  the  precipitate  was  washed  four  times 
with  9  cc.  of  solution  under  the  conditions  named  above,  only 
0.00002  gm.  would  remain,  an  amount  which  can  be  safely  neg- 
lected. 

The  formula  shows  further  that  the  efficiency  of  the  process 
decreases  greatly  as  the  volume  of  the  liquid  left  in  contact  with 
the  precipitate  increases,  and  that  the  use  of  several  portions  of 
wash  solutions  of  small  volume  is  decidedly  more  effective  than 
the  use  of  a  smaller  number  of  large  portions.  If,  the  36  cc.  of 
wash  solution  used  in  four  equal  portions  in  the  above  example  had 
been  used  as  a  single  portion  the  weight  of  impurity  still  left  in 
the  filter  would  amount  to  0.0054  gm. 

Discrepency  Between  the  Theory  and  Practice.  Experience 
does  not  agree  with  the  predictions  of  the  theory  outlined  above 
and  the  assumption  that  the  impurities  are  equally  distributed 
thruout  the  wash  solution  used  is  not  valid.  When  the  latter  is 
merely  poured  thru  the  filter  it  may  not  remain  in  contact  with 
the  precipitate  long  enough  to  bring  about  a  uniform  distribution 
of  the  soluble  salts,  and  it  is  often  difficult  to  prevent  the  formation 
of  channels  in  the  mass  of  precipitate,  especially  where  the  latter 
is  of  a  gelatinous  character,  which  prevents  the  solution  from 
coming  into  intimate  contact  with  the  soluble  impurities.  The 
only  reliable  method  of  procedure  is  to  wash  the  precipitate  until 
an  actual  test  of  the  washing  shows  that  soluble  substances  are  no 
longer  being  removed  in  appreciable  amounts.  It  is  often  con- 
venient to  ascertain  this  by  evaporating  a  reasonably  large  volume 
of  the  last  washings  (at  least  20  cc.),  to  complete  dryness  and 
noting  the  amount  of  residue  left.  In  other  cases  it  is  more 
convenient  to  test  the  washings  for  the  Compound  which  is  being 


FILTERING,  WASHING  AND  IGNITING  PRECIPITATES      127 


removed  by  an  appropriate  and  sufficiently  delicate  qualitative 
test.  It  is  usually  safe  to  assume,  however,  that  precipitates  which 
have  been  brought  down  under  identical  conditions  from  solutions 
of  the  same  composition  require  the  same  amount  of  washing,  and 
in  repeating  quantitative  processes  much  unnecessary  labor  can 
be  avoided  by  ascertaining  the  amount  of  washing  necessary  in 
the  first  determination. 

Washing  by  Decantation.  It  is  desirable  to  wash  precipitates 
which  rapidly  clog  up  the  pores  of  the  filter  in  the  original  vessel, 
that  is,  to  avoid  bringing  them  on  the  filter 
as  far  as  possible  until  the  impurities  have 
been  removed.  This  can  be  effected  by 
allowing  the  precipitate  to  settle  to  the 
bottom  of  the  vessel,  "decanting"  off  the 
clear  supernatant  liquid  thru  the  filter,  add- 
ing wash  water,  stirring  and  repeating  the 
same  cycle  of  operations  as  long  as  may 
be  necessary.  The  separation  of  precipi- 
tates of  low  density  is  often  an  extremely 
slow  process,  and  where  they  are  also  bulky, 
comparatively  large  amounts  of  solution 
must  be  left  in  contact  with  the  precipi- 
tate after  each  decantation;  on  the  other 
hand  the  wash  solution  remains  in  contact 
with  the  entire  precipitate  long  enough  FlS-  31.  —  Support 
to  insure  an  equal  distribution  of  the 


Drying  Filter 


for 


soluble  impurity  thruout  its  volume.  On  the  whole  the  process 
of  washing  by  decantation  is  slow  but  with  certain  types  of  precip- 
itate it  is  the  best  method  to  employ. 

Ignition  of  Precipitates.  The  precipitate  finally  separated  is 
necessarily  wet,  and  must  be  dried  before  it  can  be  weighed; 
frequently  it  is  retained  on  a  paper  filter,  which  must  be  burned 
up;  and  it  often  consists  of  a  mixture,  that  must  be  converted 
into  a  compound  which  has  a  definite  composition.  All  of  these 


128  QUANTITATIVE  CHEMICAL  ANALYSIS 

changes  represent  gas-evolution  processes,  and  hence  precipitation 
processes  involve  the  use  of  the  principles  discussed  in  Chapter  X. 
During  the  combustion  of  the  filter  some  of  the  precipitate  may 
be  reduced  by  the  reducing  action  of  the  carbon  monoxide  or 
volatile  hydrocarbons  formed,  or  where  the  precipitate  is  very 
fine  and  light  some  of  the  precipitate  may  be  carried  off  by  the 
air  currents  produced  and  lost.  Where  either  of  these  difficulties 
is  to  be  feared  it  is  preferable  to  dry  the  filter  before  ignition; 
most  of  the  precipitate  can  then  be  separated  from  the  filter  by 
means  of  a  fine  brush,  the  paper  burned  and  the  precipitate  which 
has  been  temporarily  set  aside  added  to  the  residue.  As  this 
procedure  involves  the  possibility  of  mechanical  losses,  it  is  pref- 
erable, where  the  precipitate  is  not  readily  reduced  and  is  not 
finely  divided,  to  place  it  while  still  moist  in  the  crucible  and  heat 
the  latter  cautiously  until  water  and  volatile  hydrocarbons  have 
been  "  smoked  off/7  and  then  burn  off  the  residual  carbon  by  direct 
ignition.  Fig.  31  represents  a  convenient  device  which  is  placed 
on  a  hot  plate  and  used  for  drying  a  paper  filter  in  the  funnel. 


CHAPTER  XVIII 

THE  PHENOMENA   OF   OCCLUSION 

Theories  Advanced  to  Explain  the  Phenomenon.  Many  pre- 
cipitates are  found  to  possess  the  property  of  retaining  certain 
soluble  constituents  of  the  solution  from  which  they  have  separated 
in  such  a  form  that  they  cannot  be  removed,  even  by  long-con- 
tinued washing.  The  phenomenon  is  a  complex  one;  three 
theories  have  been  advanced  to  explain  it. 

Schneider  suggested  that  the  soluble  salt  was  taken  up  by  the 
precipitate  as  the  latter  separated,  and  remained  distributed 
thruout  the  interior  of  the  solid  particles ;  that  is,  the  phenomenon 
is  the  result  of  the  formation  of  a  solid  solution  in  which  the 
precipitate  is  the  solvent  and  the  soluble  salt  the  solute.  If  this 
is  true  we  should  expect  to  find  definite  saturation  limits  for  every 
precipitate  with  respect  to  the  occluded  substance,  but  such 
limits  have  not  been  found  in  most  of  the  cases  which  have  been 
investigated. 

Ostwald  designates  the  phenomenon  by  the  term  "  adsorption." 
This  term  was  first  used  by  E.  du  Bois  Reymonds  to  represent  the 
retention  of  soluble  substances  by  porous  or  finely  divided  solids 
when  placed  in  solutions  containing  them.  A  typical  illustration 
of  it  is  the  well-known  property  of  bone-charcoal  of  removing 
coloring  matter  from  solutions.  According  to  the  theory  elabor- 
ated by  Ostwald  an  attractive  or  restraining  force  is  exerted  by 
the  solid,  Which  tends  to  hold  the  molecules  of  dissolved  substance 
in  the  immediate  neighborhood  of  its  bounding  surfaces,  and  either 
delays  or  entirely  prevents  the  removal  of  these  substances  by 
washing.  The  action  of  bone-charcoal  seems  to  be  remarkable 
as  the  great  majority  of  solids  possess  this  property  to  a  much 

129 


130  QUANTITATIVE  CHEMICAL  ANALYSIS 

smaller  degree.  Very  few  precipitates  absorb  coloring  matters, 
and  their  ability  to  retain  soluble  salts  is  of  a  decidedly  selective 
character. 

Richards  believes  that  the  phenomenon  is  due  to  chemical 
rather  than  physical  forces,  and  designates  it  by  the  term  "  occlu- 
sion. "  According  to  this  theory  complex  basic  salts  or  molecular 
compounds,  which  are  but  slightly  soluble,  are  formed  to  a  greater 
or  less  extent  along  with  the  desired  precipitate.  Thus  the  oc- 
clusion of  ferric  salts  by  barium  sulfate  is  explained  by  assuming 
that  the  latter  precipitate  is  contaminated  with  small  amounts  of 
a  double  sulfate  of  the  formula  BaS04  •  Fe2(S04)3  •  H20.  When  this 
compound  is  ignited  the  ferric  sulfate  is  decomposed,  and  three 
molecules  of  SOs  and  one  of  water  are  expelled,  and  one  molecule  of 
BaS04  and  one  of  Fe20s  are  obtained.  This  explains  why  the 
results  are  too  low,  when  this  salt  separates  with  the  precipitate, 
in  spite  of  the  fact  that  it  is  contaminated  with  Fe20s.  Altho  it 
is  probable  that  solid  solution  and  adsorption  are  in  many  in- 
stances concerned  with  the  phenomenon  in  question,  it  will  be 
designated  in  this  book  by  the  term  occlusion. 

Occlusion  Varies  with  the  Concentration  of  the  Soluble  Salt. 
One  of  the  most  important  and  well-established  facts  relating  to 
the  phenomenon  is  that  the  amount  of  occlusion  increases  as  the 
concentration  of  the  salt  in  the  solution  from  which  the  precipitate 
separates  increases,  but  is  not  proportional  to  that  concentration. 
Some  experiments  on  the  occlusion  of  nitrates  by  barium  sulfate 
illustrate  this  statement.  In  these  experiments  25  cc.  of  a  solution 
of  sulfuric  acid  containing  exactly  0.425  gm.  of  H2S04,  which 
should,  therefore,  yield  exactly  1.0118  gm.  of  BaS04,  were  used. 
Variable  amounts  of  potassium  nitrate  were  added  in  the  different 
experiments,  but  the  solution  was  in  every  case  diluted  to  exactly 
200  cc.,  heated  to  boiling,  and  the  BaS04  precipitated  by  the 
addition  of  50  cc.  of  a  solution  containing  1.3  gm.  of  BaCl2;  after 
standing  for  sixteen  hours  the  precipitate  was  filtered  off,  washed 
thoroughly,  ignited  and  weighed.  The  results  were  as  follows: 


THE   PHENOMENA  OF  OCCLUSION 


131 


Series  No.          

1 

2 

3 

4 

Wt.  of  KNO3  present  

0.0000 

0.2000 

1  0000 

5  0000 

Wt   of  ppt    found  (A) 

1  0131 

1  0199 

1  0308 

1  0176 

Wt   of  ppt.  found  (B)  

1.0134 

1.0160 

1  0291 

1  0468 

Average  of  A  and  B 

1  0133 

1  0180 

1  0300 

1  0472 

Excess  of  wt.  found  

0.0015 

0.0062 

0  0182 

0  0354 

A  qualitative  examination  showed  that  the  precipitates  obtained 
in  the  first  series  contained  very  slight  amounts  of  chlorides,  those 
obtained  in  the  other  series  gave  a  slight  alkaline  reaction.  It  is 
probable  that  the  1.5  mg.  in  excess  of  the  theoretical  weight 
obtained  in  the  first  series  represents  occluded  barium  chloride, 
the  much  larger  excesses  obtained  in  the  other  series  represents 
barium  oxide,  which  resulted  from  the  decomposition  of  barium 
nitrate  occluded  by  the  precipitate.  The  last  three  series  of 
experiments  show  clearly  that  the  amount  of  occlusion  increases 
with  the  concentration  of  potassium  nitrate,  but  is  not  proportional 
to  it. 

Occlusion  Takes  Place  While  the  Precipitates  Separate.  A 
second  well-established  fact  is  that  occlusion  takes  place  especially 
during  the  time  the  precipitate  is  separating  from  the  solution. 
This  was  shown  by  a  fifth  series  of  experiments,  which  were  car- 
ried on  exactly  as  those  of  the  third  series  except  that  the  1  gm.  of 
potassium  nitrate  was  added  after  the  precipitant  had  been  added 
and  the  mixture  had  been  allowed  to  stand  for  ten  minutes.  The 
weights  obtained  were  1.0140  and  1.0144  gm.  respectively.  These 
figures  show  that  the  occlusion  of  the  nitrate  was  very  small  if 
added  after  the  precipitate  had  separated  from  the  solution. 
Some  experiments  are  on  record  which  show  that  barium  sulfate 
and  other  precipitates  do  occlude  soluble  salts  even  after  they  have 
separated  from  the  solution,  but  to  a  very  slight  extent  only. 

Occlusion  Varies  with  the  Method  of  Precipitation.  A  third 
factor  which  has  a  pronounced  effect  upon  the  amount  of  occlusion 


132  QUANTITATIVE   CHEMICAL   ANALYSIS 

is  the  concentration  of  the  precipitant  used,  and  the  manner  in 
which  it  is  added.  If  a  solution  of  barium  chloride  is  added  to  a 
solution  of  sulfuric  acid  the  latter  will  in  general  be  in  excess  in  the 
resulting  mixture  up  to  the  time  at  which  an  equivalent  amount 
of  barium  chloride  has  been  added;  if  a  solution  of  sulfuric  acid 
is  added  to  a  solution  of  barium  chloride  the  latter  will  in  general 
be  in  excess  up  to  the  time  at  which  an  equivalent  amount  of 
sulfuric  acid  has  been  added.  The  former  set  of  conditions  will 
favor  the  occlusion  of  sulfuric  acid,  the  latter  of  barium  chloride. 
As  barium  chloride  is  occluded  more  readily  than  sulfuric  acid, 
and  further  is  not  appreciably  volatilized  on  ignition  whereas 
sulfuric  acid  is  completely  volatilized,  the  method  of  procedure 
first  named  might  be  expected  to  yield  lower  results  than  the  one 
named  last.  This  was  shown  "in  a  sixth  series  of  experiments  in 
which  the  conditions  of  the  first  series  were  maintained  except  that 
the  sulfuric  acid,  diluted  to  200  cc.  was  added  to  the  barium 
chloride,  diluted  to  50  cc.  The  results  obtained  were  1.0249  and 
1.0212.  In  series  1,  owing  to  the  dilution  of  the  solution  to  which 
the  precipitating  agent  was  added  occlusion  of  sulfuric  acid  was 
small  and  was  more  than  counterbalanced,  that  is,  to  the  extent 
of  1.5  mg.,  by  the  occlusion  of  barium  chloride.  In  the  sixth  series 
on  the  contrary,  the  occlusion  of  sulfuric  acid  was  reduced  to  a 
minimum,  while  the  occlusion  of  barium  chloride  was  at  a  maximum 
and  hence  the  average  result  was  nearly  12  mg.  too  high. 

It  should  be  noted  that  it  is  impossible  to  insure  an  absolutely 
uniform  distribution  of  the  precipitating  agent  thruout  the  mixture 
during  the  time  it  is  being  added.  There  is  a  pronounced  tendency 
for  the  concentration  of  both  reagents  to  exceed  temporarily  the 
average  concentration  of  the  entire  mixture  at  certain  portions 
of  the  solution.  For  this  reason,  some  of  the  precipitate  may 
separate  in  the  presence  of  a  much  greater  concentration  of  one 
reagent  or  the  other  than  corresponds  to  its  average  composition, 
and  the  effect  of  mixing  the  two  reagents  in  the  predetermined 
order  may  be  greatly  diminished.  These  difficulties  may  be 


THE  PHENOMENA  OF  OCCLUSION  133 

largely  avoided  by  using  dilute  solutions,  by  adding  the  precipitant 
very  slowly,  and  by  stirring  vigorously  while  it  is  being  added. 
Complete  separation  of  the  precipitate  also  requires  an  appreciable 
time  interval,  and  if  the  rate  at  which  it  separates  is  less  than 
that  at  which  the  reagent  is  added,  much  of  the  precipitate  may 
separate  in  the  presence  of  an  unduly  large  concentration  of  the 
reagent.  In  the  experiments  described  above  the  barium  chloride 
was  added  during  an  interval  of  ten  seconds,  and  altho  the  mix- 
ture was  stirred  vigorously  while  the  reagent  was  being  added, 
even  in  experiment  1  an  excess  of  1.5  mg.  was  obtained.  The 
actual  amount  of  chloride  occluded  by  the  precipitate  included 
not  only  the  excess  of  1.5  mg.  but  also  the  normal  deficiency  due 
to  the  solubility  of  the  precipitate,  which  probably  represented  1 
or  2  mg.  more.  It  could  have  been  greatly  reduced  by  adding  the 
precipitant  more  slowly  and  by  reducing  the  excess  added.  This 
was  actually  shown  to  be  the  case  in  a  seventh  series  of  experi- 
ments in  which  the  precipitations  were  made  under  the  same  con- 
ditions as  the  first  series,  excepting  that  the  precipitant  was  added 
drop  by  drop  during  an  interval  of  twenty  minutes.  The  weights 
obtained  were  1.0102  and  1.0095. 

Owing  to  the  extreme  difficulty  of  obtaining  absolutely  identical 
conditions  with  respect  to  these  factors  decided  differences  in  the 
amount  of  occlusion  may  result,  even  where  the  attempt  is  made 
to  carry  out  the  determinations  under  parallel  conditions.  This 
is  largely  responsible  for  the  variations  which  appear  in  some  of 
the  series  of  experiments  here  described,  these  variations  are 
especially  large  where  the  total  amount  of  occlusion  is  also  large. 

What  Salts  Are  Occluded.  Certain  ions  are  largely  occluded, 
others  to  a  slight  extent  only.  This  is  shown  in  the  following  series 
of  experiments,  which  were  made  under  the  same  conditions  as 
the  first  series,  excepting  that  amounts  of  chlorides  on  the  one 
hand  and  of  nitrates  on  the  other  sufficient  to  yield  equal  concen- 
trations of  Cl  and  NO3  ions,  respectively,  were  introduced  into  the 
solution  before  precipitation. 


134 


QUANTITATIVE  CHEMICAL  ANALYSIS 


Series  No... 


10 


Salt  added.... 
Wt.  of  ppt.  A . 
Wt.  of  ppt.  B. 
Avg.  A  and  B. 
Error . . , 


0.0000 
1.0131 
1.0134 
1.0133 
+0.0015 


0.37HC1 
1.0135 
1.0143 
1.0139 
+0.0021 


0.59NaCl 
1.0088 
1.0103 
1.0096 
-0.0022 


0.75KC1 
1.0054 
1.0064 
1.0059 
-0.0059 


Series  No. . 


12 


13 


14 


Salt  added 

Wt.  of  ppt.  A. 
Wt.  of  ppt.  B. 
Avg.  A  and  B . 
Error . . , 


0.54(NH4)C1 
1.0080 
1.0091 
1.0086 
-0.0032 


0.56CaCl2 
0.9954 
0.9961 
0.9958 
-0.0160 


0.48MgCl2 
1.0140 
1.0155 
1.0148 
+0.003 


0.0000 
1.0136 
1.0137 
1.0137 
+0.0019 


Series  No.. 


16 


17 


Salt  added.... 
Wt.  of  ppt.  A . 
Wt.  of  ppt.  B. 
Avg.  A  and  B. 
Error . . , 


0.63HN03 
1.0376 
1.0400 
1.0388 
+0.0270 


0.85NaNO3 
1.0368 
1.0413 
1.0391 
+0.0273 


i.o  KNO, 

1.0308 

1.0291 

1.0300 

+0.0182 


Series  No.. 


19 


20 


21 


Salt  added 

Wt.  of  ppt.  A. 
Wt.  of  ppt.  B. 
Avg.  A  and  B . 
Error.., 


1.0244 

1.0238 

1.0241 

+0.0123 


0.82Ca(NO3)2 
1.0144 
1.0174 
1.0159 
+0.0041 


0.73Mg(NO3)2 
1.0339 
1.0330 
1.0335 
+0.0217 


By  comparing  the  entire  series  of  results  in  which  chlorides  were 
present  with  the  series  in  which  equivalent  concentrations  of 
nitrates  were  present  it  is  apparent  that  the  substitution  of  N03 
for  Cl  ions  increased  the  total  weight  of  precipitate  found  by  an 
approximately  equal  amount.  The  very  high  results  obtained 
when  even  moderate  amounts  of  most  of  the  nitrates  used  were 
present  are  evidently  due  to  the  fact  that  the  precipitates  contained 
nitrates  in  addition  to  BaS04,  probably  as  the  result  of  the  forma- 


THE  PHENOMENA  OF  OCCLUSION  135 

tion  of  complex  compounds.  It  is  not  improbable  that  the  S04 
ions  possess  an  appreciable  tendency  to  unite  with  electrically 
neutral  Ba(N03)2  molecules  and  that  the  complex  ion  formed  unites 
with  Ba  ions  to  form  a  salt  of  the  formula  BaSO4  •  Ba(N03)2,  or  that 

the   solution   contained  small  concentrations  of  ions  having  the 

+ 
formula  BaN03  which  combined  with  S04  to  form  (BaN03)2S04.* 

The  probability  of  such  reactions  as  these  would  be  determined 
for  the  most  part  by  the  solubility  of  the  hypothetical  com- 
pound, as  compared  with  that  of  BaS04.  The  occlusion  of 
chlorides  may  be  due  to  an  analogous  series  of  reactions,  but  the 
tendency  for  these  reactions  to  take  place  is  decidedly  less. 

A  comparison  of  the  results  obtained  in  series  9  and  16  with  those 
obtained  in  8  and  15  indicates  that  the  occlusion  of  hydrogen  gives 
low  results,  that  is,  reduces  to  an  appreciable  extent  the  high 
results  due  to  the  occlusion  of  chlorides  and  nitrates.  This  may 

arise  from  the  presence  of  ions  of  the  formula  HS04  which  unite 

+  + 
with  Ba  to  form  (HS04)2Ba;  this  theory  is  in  accord  with  the  fact 

that  such  precipitates  yield  very  small  amounts  of  sulfuric  acid 
when  ignited. 

A  comparison  of  the  results  obtained  in  the  remaining  series 
of  experiments  with  those  obtained  in  series  8  and  15  show  that 
the  sodium,  potassium,  ammonium  and  calcium  ions  all  give  low 
results  but  the  magnesium  ion  does  not  affect  the  results  appreci- 
ably. The  probable  explanation  is  in  all  cases  the  formation  of 
compounds  similar  to  Na2S04  •  BaS04,  that  is,  the  formation  of 
double  salts  in  which  a  metal  having  a  lower  atomic  weight  than 
that  of  barium  is  substituted  for  that  element.  The  tendency 
for  the  formation  of  these  double  salts  varies  greatly;  it  is  at  a 
maximum  where  calcium  is  present. 

Methods  of  Avoiding  the  Error  from  Occlusion.  It  is  impos- 
sible to  predict  to  what  extent  a  given  substance  will  be  occluded 

*  Hulett  and  Duschak,  Zeit.  fur  anorganische  Chemie,  40,  196  (1904). 


136  QUANTITATIVE  CHEMICAL  ANALYSIS 

by  a  given  precipitate  and  even  where  the  error  from  this  source 
is  known  to  be  large  it  is  difficult  to  avoid  or  overcome  it. 

If  the  ion  in  question  is  occluded  but  slightly  and  the  solubility 
of  the  precipitate  is  very  small  the  error  can  often  be  reduced  to 
negligible  proportions  by  making  the  precipitation  from  a  suffi- 
ciently diluted  solution.  In  some  cases  it  is  preferable  to  remove 
the  ion  which  is  occluded  by  an  evaporation  process,  or  to  replace 
it  by  another  ion  which  is  occluded  to  a  smaller  extent  by  the  use 
of  a  reagent  which  renders  it  insoluble,  or  converts  it  into  a  gas. 
In  other  cases  it  is  possible  to  reduce  the  concentration  of  the  ion 
that  is  occluded  by  adding  reagents  which  reduce  its  degree  of 
ionization. 

In  many  cases  it  becomes  necessary  to  purify  the  precipitate 
containing  the  occluded  compound  by  dissolving  and  reprecipitat- 
ing  under  more  favorable  conditions,  that  is,  by  the  process  of 
"  double  precipitation. "  The  difficulty  with  this  method  is  to 
find  a  solvent  which  dissolves  the  precipitate  readily  without 
introducing  large  concentrations  of  other  ions,  which  are  also 
largely  occluded. 


CHAPTER  XIX 

GENERAL  THEORY   OF  ELECTROLYTIC   SEPARATIONS 

Chemical  Changes  Effected  by  the  Electric  Current.     The 

transmission  of  an  electric  current,  of  a  sufficiently  high  intensity, 
thru  a  solution  of  an  electrolyte  is  associated  with  physical  and 
chemical  changes,  some  of  which  can  be  used  to  advantage  in 
quantitative  analysis. 

The  chemical  effect  at  the  cathode  is  always  some  form  of 
reduction.  The  hydrogen  ion  here  loses  its  positive  charge,  and 
either  forms  gaseous  hydrogen  or  acts  directly  as  a  reducing  agent. 
Certain  metallic  ions,  such  as  ferric  and  stannic  ions,  either  first 
lose  a  part  of  their  charges  and  form  ferrous  and  stannous  ions, 
or  separate  as  metals.  Certain  other  metallic  ions,  such  as  those 
of  the  alkali  group,  are  first  reduced  to  the  metallic  state,  but  the 
resulting  metals  react  with  water  to  form  hydrogen  and  an  alkaline 
hydroxide. 

The  chemical  effect  at  the  anode  is  always  some  form  of  oxida- 
tion. The  anions  of  the  halogen  group  are  liberated  as  such  and 
act  directly  as  oxidizing  agents.  The  SO 4  ion  decomposes  into 
sulfur  trioxide  and  oxygen,  but  the  former  reacts  with  water  and 
forms  sulfuric  acid;  the  NOs  ion  decomposes  into  nitrogen  pent- 
oxide  and  oxygen,  but  the  former  reacts  with  water  and  forms 
nitric  acid.  The  oxygen  thus  liberated  may  separate  as  a  gas  or 
may  act  as  an  oxidizing  agent.  Altho  in  general  the  simple 
metallic  ions  separate  as  such  at  the  cathode,  lead,  manganese  and 
thallium  ions  separate  at  the  anode  in  the  form  of  insoluble  per- 
oxides, especially  if  the  concentration  of  the  hydrogen  ions  is  small. 

Metals  Which  Can  Be  Determined.  Under  certain  conditions 
the  metals  precipitated  at  the  cathode,  and  the  peroxides  precip- 

137 


138  QUANTITATIVE  CHEMICAL  ANALYSIS 

itated  at  the  anode  adhere  to  the  electrode  firmly,  and  the  weight 
of  the  metal  or  oxide  precipitated  can  then  be  determined  readily, 
if  the  weight  of  the  electrode  is  known.  The  necessity  of  filtration, 
which  forms  a  troublesome  feature  of  many  quantitative  processes 
is  thereby  avoided.  A  large  number  of  factors  affect  the  rapidity 
and  completeness  with  which  the  different  metals  are  precipitated, 
as  well  as  the  physical  properties  and  purity  of  the  resulting 
precipitate.  Thus  far  electrolytic  methods  have  been  most  suc- 
cessfully applied*  to  the  determination  of  copper,  mercury,  silver, 
antimony,  tin,  iron,  nickel,  cobalt,  cadmium  and  zinc  as  metals, 
and  of  lead  and  manganese  as  oxides. 

The  Voltage  Needed.  If  the  difference  of  potential  between 
two  electrodes  immersed  in  a  solution  of  an  electrolyte  is  small 
a  barely  perceptible  current  passes  thru  the  solution;  if  the  po- 
tential difference  is  gradually  increased  a  point  is  finally  reached 
at  which  the  amount  of  current  carried  by  the  solution  shows  a 
marked  increase,  which  corresponds  to  the  point  at  which  the  ions 
present  first  begin  to  lose  their  charges.  This  voltage  represents 
the  so-called  "  decomposition  voltage "  of  the  electrolyte  con- 
cerned. Its  value  is  mainly  dependent  upon  the  algebraic  sum 
of  the  numbers  representing  the  voltages  necessary  to  separate 
the  element  or  radical  composing  the  anion  and  cation  from  their 
respective  charges.  It  depends  further  upon  the  concentration 
of  the  solution,  the  temperature,  and  to  a  slight  extent  upon  the 
size  and  distance  between  the  two  electrodes  and  the  metal  of 
which  they  are  composed.  Decreasing  the  concentration  by  the 
factor  ten  increases  the  value  of  the  decomposition  voltage  by 

-  volts,  in  which  n  represents  the  valence  of  the  ion  concerned. 

It  is  difficult  to  determine  these  values  accurately,  owing  to  the 
large  number  of  variables  concerned,  and  the  fact  that  disturbing 

*  The  literature  of  electrochemical  processes  is  extensive.  Summaries  of 
the  more  important  methods  will  be  found  in  Edgar  F.  Smith's  Electrochemical 
Analysis  and  Alexander  Classen's  Quantitative  Analysis  by  Electrolysis. 


GENERAL  THEORY  OF  ELECTROLYTIC  SEPARATIONS      139 

secondary  actions  often  take  place.  The  approximate  values  of 
the  voltages  necessary  to  deprive  some  of  the  more  important  ions, 
in  solutions  of  normal  concentration,  at  ordinary  temperatures, 
of  their  charges  are  as  follows: 

Al          Zn         Cd          Fe          Ni         Pb          H          Cu          Sb          Hg         Ag        SO« 
+1       +0.49    +0.14    +0.06    -0.05    -0.13    -0.28    -0.61    -0.75    -1.03    -1.05    +2.18 

From  this  table  it  is  easy  to  calculate  that  it  would  be  necessary 
to  maintain  a  difference  of  potential  greater  than  1.57  volts  in 
order  to  cause  metallic  copper  to  separate  from  a  solution  contain- 
ing normal  concentrations  of  Cu  and  S04  ions,  but  as  the  copper 
is  deposited  the  concentration  of  the  copper  ions  continually 
decreases,  and  this  necessitates  a  continuous  tho  slight  increase 
in  the  voltage  used,  if  the  separation  is  to  be  even  approximately 
complete.  This  fact  is  not  of  especial  importance  unless  the 
solution  also  contains  other  metallic  ions,  which  have  a  slightly 
greater  decomposition  voltage.  In  this  case  it  may  be  impossible 
to  completely  separate  one  metal  without  using  a  voltage  which 
causes  the  second  metal  to  begin  to  separate  also.  In  general, 
only  those  metals  whose  decomposition  voltages  differ  by  several 
tenths  of  a  volt,  can  be  separated  from  each  other  by  maintaining 
a  constant  voltage  during  the  electrolysis.  The  addition  of  certain 
reagents,  such  as  potassium  cyanide,  to  solutions  containing  two 
metals  sometimes  reduces  the  concentration  of  one  metallic  ion 
to  a  greater  extent  than  the  other,  and  makes  it  possible  to  carry 
out  the  separation  by  the  "  constant  voltage  "  method  which  would 
otherwise  be  impossible. 

The  voltage  used  also  affects  the  current  strength,  for  according 
to  Ohm's  law  the  strength  (expressed  in  amperes)  must  equal  the 
tension  (expressed  in  volts)  divided  by  the  resistance  (expressed 
in  ohms).  In  a  circuit  in  which  electrolysis  is  being  effected  the 
voltage  actually  available  is  diminished  by  the  decomposition 
voltage  of  the  electrolyte  decomposed;  hence  the  current  strength 
actually  available  is  represented  by  the  voltage  available  minus 


140  QUANTITATIVE  CHEMICAL  ANALYSIS 

the  decomposition  voltage  of  the  electrolyte  divided  by  the  resist- 
ance of  the  circuit. 

Forms  of  Electrodes  Used.  Electrodes  of  platinum  are  to  be 
preferred  to  those  of  any  of  the  more  common  metals,  since  they 
can  be  ignited  directly  in  the  flame,  are  not  attacked  by  solutions 
of  acids  or  alkalies  during  electrolysis,  and  can  be  treated  for  the 
removal  of  the  precipitated  metal  after  electrolysis  with  strong 
acids.  Owing  to  the  cost  of  the  metal  the  cathode  should  be  as 
light  as  possible  for  the  surface  exposed;  it  should  also  have  such 
a  form  as  to  favor  circulation  of  the  solution  as  much  as  possible; 
and  should  be  capable  of  being  easily  removed  from  the  solution, 
washed  and  weighed.  Some  of  the  types  of  electrodes  in  general 
use  are  described  below. 

The  Classen  dish  represented  in  Fig.  32  serves  to  contain  the 
solution  being  electrolyzed,  and  is  itself  made 
the  cathode;   the  anode  used  with  it  is  a  disk  of 
foil  or  a  horizontally  coiled  spiral  of  wire.     The 
size  in  general  use  has  a  capacity  of  220  cc.  and 
weighs  about  37  gm.     This  arrangement  is  not 
favorable  to  circulation  of  the  solution;  further, 
the  removal  of  the  solution  and  washing  of  the 
precipitated  metal   is  not    conveniently   carried 
Fig  32.  — Classen  out.     Its  chief  advantage  is  that  many  deposits 
which,  even  under  favorable  circumstances,  are 
but  poorly  adherent  are  more  easily  retained  by  it  without  loss 
than  by  other  forms. 

The  Mansfeld  electrode  shown  in  Fig.  33  consists  of  a  cylinder 
of  thin  foil  usually  about  5  cm.  hi  length  and  2^  cm.  in  diam- 
eter, soldered  with  gold  to  a  supporting  wire.  The  anode  used 
with  it  consists  of  a  cylindrically  coiled  spiral  of  wire  placed  in 
the  center  of  the  cylinder,  or  a  horizontally  coiled  spiral  placed 
at  the  bottom  of  the  containing  vessel.  If  the  former  anode 
is  used,  that  portion  of  the  solution  which  is  surrounded  by  the 
cathode  is  effectively  stirred  by  the  currents  produced  by  the  gas 


GENERAL  THEORY  OF  ELECTROLYTIC   SEPARATIONS      141 


liberated  at  the  anode;  these  currents  affect  the  annular  space  out- 
side the  cathode  to  a  slight  extent  only,  and  a  much  larger  per- 
centage of  the  deposit  separates  on  the  inside 
than  on  the  outside  of  the  cylinder.  The  un- 
equal distribution  of  the  action  of  the  current 
over  the  surface  is  often  shown  by  the  appear- 
ance of  a  spongy  deposit  on  the  lower  edges  of 
the  cylinder,  whereas  the  other  portions  of  the 
deposit  .are  smooth  and  adherent.  Its  efficiency 
may  be  greatly  increased  by  drilling  a  large 
number  of  holes  in  the  cathode.  If  the  horizontal 
form  of  anode  is  used  the  circulation  of  the 
solution  is  more  equally  distributed  but  is  still 
very  poor. 

The  Winkler  electrode  shown  in  Fig.  34  con-  Fig.  33.  —  Mans- 
sists  of  a  cylinder  of  fine  gauze  supported  by  a  feld  Electrodes 
wire  of  small  diameter.  The  form  represented  is  3  cm.  in  diameter 
and  6  cm.  in  length,  the  gauze  is  composed  of  wires  0.06  mm. 
in  diameter  with  41  meshes  per  linear  centimeter. 
Unlike  the  Mansfeld  form  it  offers  practically  no 
barrier  to  the  circulation  of  the  solution  and 
hence  the  deposition  is  much  more  rapid,  and 
there  is  comparatively  little  danger  of  obtaining 
spongy  deposits. 

The  use  of  a  small  amount  of  mercury,  which 
is  placed  in  the  bottom  of  the  beaker  or  flask 
containing  the  solution,  and  connected  with  the 
battery  by  means  'of  a  platinum  wire,  as  a  cathode, 
has  been  suggested  and  used  to  some  extent.*     It- 
has  advantages  over  the  other  form  of  cathodes  in 
Fig.  347^Winkler  the  precipitation  of  metals  which  give  poor  deposits 
Cathode          or   are   acted   upon   by  the   solution.     Its   com- 

*  See  especially  Hildebrand,  Jour.  Amer.  Chem.  Soc.,  25,  883  (1903)  and 
29,  1445  (1907). 


142 


QUANTITATIVE   CHEMICAL   ANALYSIS 


paratively  large  weight  and  the  need  of  great  care  in  washing  and 
drying  before  weighing  make  it  less  convenient  than  the  other 
forms. 

The  comparative  efficiencies  of  the  first  three  electrodes  de- 
scribed above  are  shown  in  the  following  table,*  which  gives  their 
approximate  weights,  available  surfaces  and  the  length  of  time 
needed  for  the  precipitation  of  0.1975  gm.  of  copper  under  identical 
conditions. 


Cathode  used 

Surface 
exposed 

Weight  of 
cathode 

Time 
required 

Classen  dish     

Sq.  cm. 
100 

Gm. 
37 

Minutes 

400 

Mansfeld  cathode  

79 

11 

450 

Mansfeld  cathode  with  holes   .  .  . 

78 

11 

390 

V\  inkier  cathode  

93 

4  2 

50 

Effect  of  Varying  Current  Strength.  The  amount  of  metal 
separated  from  the  solution  during  a  given  time  interval  depends 
upon  the  rate  at  which  the  charges  on  the  electrodes  are  renewed; 
that  is,  upon  the  quantity  of  electricity  which  flows  thru  the  solu- 
tion during  a  given  time  interval.  Hence  the  rate  at  which  the 
metal  is  deposited  depends  upon  the  current  strength,  as  measured 
in  amperes.  The  law  of  Faraday  states  that  the  amounts  of 
different  metals  separated  by  the  same  current  during  the  same 
time  interval  is  directly  proportional  to  their  atomic  weights  and 
inversely  proportional  to  their  valencies.  A  current  of  one  ampere 
passing  thru  a  solution  of  a  silver  salt  for  one  hour  deposits  4.026 
gm.  of  silver  and  equivalent  amounts  of  other  metals.  This  law 
might  be  used  to  calculate  the  time  needed  for  complete  deposition 
of  all  of  the  metal  present  if  all  of  the  current  which  passes  thru  the 
solution  was  carried  by  the  electrolyte  whose  cation  is  being 
deposited.  Since,  however,  the  concentration  of  the  solution  with 

*  The  data  quoted  in  this  and  the  following  paragraphs  are  given  in  detail 
in  Jour.  Amer.  Chem.  Soc.,  32,  1264  (1910). 


GENERAL  THEORY  OF  ELECTROLYTIC   SEPARATIONS      143 


respect  to  the  metal  which  is  being  determined  gradually  decreases 
and  must  finally  become  nearly  zero,  the  resistance  of  the  solution 
and  its  decomposition  voltage  must  gradually  rise  and  finally  reach 
a  point  at  which  other  ions  begin  to  lose  their  charges  and  take 
part  in  the  transport  of  the  current.  The  law  of  Faraday  is  valid 
only  when  the  concentration  of  the  ion  which  is  being  deposited 
is  so  great  that  a  sufficient  num-  Milligrams  of  copper 
ber  of  these  ions  are  within  the 
sphere  of  attraction  of  the  elec- 
trode to  neutralize  the  charges 
on  the  electrode.  Since  circula- 
tion of  the  solution  brings  these 
ions  into  the  sphere  of  attraction 
of  the  electrode  it  favors  the  de- 
position of  the  ions  which  have 
smaller  decomposition  voltages. 

The  effect  of  increasing  the 
current  strength  upon  the  rate 
of  deposition  is  illustrated  by  the 
curves  shown  in  Fig.  35.  The 
solutions  used  contained  in  every 
case  0.1975  gm.  of  copper  as 
sulfate,  2  gm.  of  ammonium 
nitrate  and  4  cc.  of  concentrated 
nitric  acid,  and  were  diluted  to 
140  cc.  Winkler  gauze  electrodes 


VARYING  CURRENT  STRENGTH 

1    Rate    w  th     .19  Amperes 
.34         " 
.50          " 
.75 
5.50 


10  20  30  40  50  60  70  80  90100  Minutes 

Fig.  35.  —  Curves  Showing  Rate  at 
which  Copper  is  Precipitated 


were  used  and  current  strengths  of  0.19,  0.34,  0.5,  0.78  and  5.5 
amperes,  respectively,  were  maintained  continuously  thruout  the 
different  experiments. 

Increasing  the  current  strength  also  increases  the  probability 
of  obtaining  spongy  deposits,  which  are  difficult  to  weigh  accu- 
rately. In  some  cases  this  seems  to  be  due  to  the  inability  of  the 
metal  to  form  a  continuous  layer  if  deposited  too  rapidly,  in  others 
to  the  fact  that  hydrogen  is  deposited  to  a  greater  or  less  extent 


144 


QUANTITATIVE  CHEMICAL  ANALYSIS 


Milligrams  of  Copper 


with  the  metal.  The  maximum  current  strength  which  can  be 
safely  employed  increases  in  direct  proportion  to  the  surface  of 
the  cathode  available.  In  expressing  the  proper  conditions  for 
the  separation  of  a  given  metal  it  is  customary  to  express  the 
permissible  current  strength  writh  reference  to  the  so-called  "  normal 
density ,"  which  represents  the  ratio  between  the  current  used  in 

amperes,  and  the  cathode  sur- 
face exposed  in  units  of  100  sq. 
cm.  A  current  of  one  ampere 
used  with  a  cathode  exposing 
100  sq.  cm.  would  represent  a 
normal  density  of  one;  doub- 
ling both  amperage  and  cath- 
ode surface  would  not  affect 
the  normal  density;  doubling 
the  amperage  would  double  it; 
doubling  the  cathode  surface 
would  halve  it. 

Effect  of  Varying  Concen- 
tration. The  effect  of  varying 
concentration  on  the  rate  of 
precipitation  is  shown  by  the 
curves  of  Fig.  36.  The  solu- 
tions used  in  these  experi- 
ments contained  0.1975  gm. 
of  copper  as  sulfate  and  were 
diluted  to  70,  140,  210  and 
280  cc.,  respectively.  They  also  contained  1  cc.  of  concentrated 
nitric  and  2  cc.  of  concentrated  sulfuric  acid  for  each  140  cc.  of 
solution  present.  A  Winkler  gauze  electrode  and  a  current  of  0.34 
ampere  were  used  in  all  experiments. 

These  curves  show  that  the  rate  of  precipitation  decreases 
rapidly  as  the  concentration  decreases,  which  is  partly  due  to  the 
fact  that  with  the  greater  concentrations  a  greater  percentage 


10  20  30  40  50  60  70  80  90100    Minutes 

Fig.  36.  —  Curves  Showing  Rate  at 
which  Copper  is  Precipitated 


GENERAL  THEORY  OF  ELECTROLYTIC  SEPARATIONS      145 

of  the  current  used  was  carried  by  the  copper  ions  than  by  the 
hydrogen  ions.  Since  rapid  circulation  of  the  solution  reduces 
to  some  extent  the  effect  of  decreasing  concentration,  and  since 
the  circulation  of  the  solution  depends  upon  the  convection  cur- 
rents produced  by  the  gases  liberated  at  the  electrodes,  part  of  the 
effect  here  shown  is  due  to  the  fact  that  the  larger  volumes  are 
less  efficiently  stirred.  It  is  desirable,  therefore,  to  keep  the  volume 
of  the  solution  as  small  as  possible,  that  is,  just  sufficient  to  cover 
the  electrodes. 

The  Composition  of  the  Solution  Used.  Since  the  rate  of 
precipitation  depends  upon  the  concentration  of  the  metallic  ion 
which  is  to  be  precipitated,  the  addition  of  any  other  salts  that 
are  capable  of  forming  complex  ions  containing  that  metal  should 
be  avoided.  The  simple  nitrates  and  sulfates  are  usually  to  be 
preferred  as  electrolytes,  owing  to  their  comparatively  large  dis- 
sociation constants.  The  use  of  nitrates  as  electrolytes,  and  in 
general  the  presence  of  N03  ions,  has  the  further  advantage  of 
reducing  the  danger  of  obtaining  spongy  deposits,  since  the  hydro- 
gen liberated  at  the  cathode  is  at  once  reduced  by  the  solution  and 
does  not  contaminate  the  deposited  metal. 

The  presence  of  halogen  salts  in  addition  to  an  acid  has  usually 
been  avoided,  unless  the  concentration  of  the  former  is  extremely 
small,  since  the  free  halogen  which  is  liberated  at  the  anode  may 
attack  the  platinum,  and  the  resulting  platinum  ions,  which  have 
a  low  decomposition  voltage,  may  be  precipitated  with  the  desired 
metal.  Further,  the  presence  of  halogen  ions  sometimes  results 
in  the  formation  of  spongy  deposits.  These  difficulties  can  be 
avoided  by  the  addition  of  a  sufficiently  strong  reducing  agent. 

It  is  often  necessary,  however,  to  deposit  metals  from  solutions 
of  their  complex  salts.  Silver  gives  very  poor,  crystalline  deposits 
when  separated  from  solutions  of  its  simple  salts,  but  good  ones 
when  in  the  form  of  double  cyanides  or  oxalates.  Iron  and  zinc 
are  not  easily  precipitated  completely  in  the  presence  of  even  a 
small  amount  of  an  acid,  but  form  double  oxalates  from  which 


146  QUANTITATIVE  CHEMICAL  ANALYSIS 

they  are  readily  precipitated.  In  all  these  cases  the  small  amounts 
of  simple  metallic  ions  present  are  removed  by  the  action  of  the 
current,  the  decrease  in  the  concentration  of  the  simple  ions  causes 
the  complex  ions  to  break  down  into  simpler  ones  and  ultimately 
the  precipitation  is  complete. 

The  addition  of  an  acid  to  a  solution  frequently  makes  it  possible 
to  separate  one  of  the  metals  present  in  a  solution  which  contains 
several  metals  in  a  pure  condition.  If  the  hydrogen  ion  con- 
centration of  such  a  solution  is  made  sufficiently  large  and  the 
amperage  is  kept  constant  none  of  the  metallic  ions  having  a 
decomposition  voltage  greater  than  that  of  hydrogen  can  sepa- 
rate. This  is  the  principle  upon  which  the  so-called  "  constant 
current"  method  of  separating  metals  by  the  electric  current  is 
based. 

Apparatus  for  Carrying  on  a  Single  Determination  at  a  Time. 
A  special  form  of  stand  is  needed  to  support  the  anode  and  cathode 
in  the  solution,  and  provide  an  easy  method  of  connecting  the 
former  with  the  positive  and  the  latter  with  the  negative  pole  of 
the  battery.  Short-circuiting  of  the  current  thru  the  stand  is 
usually  avoided  by  making  the  central  rod  supporting  the  two 
arms  to  which  the  electrodes  are  clamped  out  of  glass. 

The  voltage  available  should  be  sufficiently  high  to  overcome 
the  counter  electromotive  force  of  the  electrolyte  and  the  external 
resistance  of  the  circuit,  and  yield  a  current  of  sufficient  strength 
to  deposit  the  metal  within  a  reasonable  length  of  time.  It  is 
further  desirable  that  the  voltage  available  be  much  greater  than 
that  actually  needed,  for,  by  introducing  a  variable  resistance  or 
" rheostat"  in  the  circuit,  currents  of  a  wider  range  of  strengths  are 
available.  These  conditions  are  easily  satisfied  by  the  use  of  a 
storage  battery  or  a  series  of  galvanic  cells  which  can  be  depended 
on  to  yield  an  approximately  constant  voltage  for  a  long  period 
of  time.  Two  storage  cells  of  the  usual  lead]  [lead  peroxide  type 
which  give  about  4.4  volts  or  four  Daniell  cells  suffice  for  the 
usual  range  of  determinations  made. 


GENERAL  THEORY  OF  ELECTROLYTIC  SEPARATIONS      147 

In  order  to  determine  whether  the  necessary  conditions  are  being 
complied  with,  an  " ammeter"  showing  the  current  strength  should 
be  introduced  into  the  main  circuit,  and  a  "  voltmeter,"  showing 
the  difference  of  potential  between  electrodes  should  be  connected 
in  a  shunt  circuit.  The  proper  arrangement  of  the  various  parts 
of  the  apparatus  is  shown  in  Fig.  37. 

Apparatus  for  Carrying  on  Several  Determinations  at  the 
Same  Time.  Although  several  solutions  may  be  electrolyzed  in 
the  same  circuit  if  a  sufficiently  large  voltage  is  used,  the  same 


Fig.  37.  — Apparatus  for  a  Single  Electrolytic  Determination 


current  necessarily  passes  thru  all,  and  if  several  different  metals 
are  being  precipitated  it  may  be  impossible  to  satisfy  the  proper 
conditions  for  each.  Furthermore,  after  precipitation  in  any  of 
the  solutions  has  been  completed,  the  current  must  be  interrupted 
while  the  electrodes  are  being  removed,  possibly  permitting  much 
of  the  precipitate  in  some  of  the  other  solutions  to  redissolve. 
For  these  reasons  it  is  necessary  to  split  up  the  main  circuit  into 
as  many  shunt  circuits  as  there  are  determinations  to  be  made. 
If  all  these  solutions  offer  the  same  counter  electromotive  force 
and  resistance,  the  current  passing  thru  each  shunt  circuit  would 
be  the  same  and  could  be  easily  regulated  by  varying  the  number 
of  battery  cells  used,  or  by  introducing  resistance  in  the  main 


148 


QUANTITATIVE  CHEMICAL  ANALYSIS 


circuit.  If  the  different  solutions  offer  varying  counter  electro- 
motive forces  and  resistances  the  current  flowing  thru  each  shunt 
circuit  must  be  regulated  by  a  separate  resistance.  By  using  the 
proper  switches  and  making  the  necessary  connections  the  same 
set  of  measuring  instruments  may  be  used  for  the  entire  series  of 
shunt  circuits.  Such  an  arrangement  is  presented  in  Fig.  38 


1   , 


Fig.  38.  — Plan  of  Wiring  of  Bench  for  Electrolytic  Determinations 


showing  two  out  of  any  desired  number  of  the  shunt  circuits,  each 
of  which  is  provided  with  a  separate  rheostat,  and  the  connections 
by  which  either  of  two  ammeters  or  a  voltmeter  may  be  thrown 
in  or  out  of  the  circuit.  One  of  these  ammeters  is  used  for  the 
measurement  of  currents  exceeding  an  entire  ampere,  the  other 


GENERAL  THEORY  OF  ELECTROLYTIC   SEPARATIONS      149 

for  fractions.     The  wires  used  for  the  connections  are  of  copper 
and  so  large  that  their  resistance  may  be  disregarded. 

The  Use  of  Mechanical  Stirring  Devices.*  It  has  already 
been  shown  that  the  efficiency  of  the  current  used  is  increased  by 
improving  the  circulation  of  the  solution.  It  is  also  easy  to  show 
that  improving  the  circulation  permits  of  the  use  of  currents  of 
much  higher  normal  densities  than  would  otherwise  give  satis- 
factory deposits  under  normal  conditions.  It  becomes  possible, 
therefore,  to  make  precipitations  with  extreme  rapidity  by  stirring 
the  solution  with  a  mechanical  stirrer  and  using  very  strong 
currents,  that  is,  from  six  to  ten  amperes.  The  stirrer  used  may 
be  a  small  paddle  wheel  of  glass  rotated  by  a  small  electric  motor 
or  the  anode  or  cathode  may  be  made  of  such  a  form  that  they 
can  be  rotated  by  the  same  means. 

*  An  excellent  summary  of  the  methods  and  results  obtained  with  such 
devices  will  be  found  in  A.  Fisher's  Electroanalytische  Schnellmethoden. 


CHAPTER  XX 

DETERMINATION   OF   CHLORINE   IN   SODIUM   CHLORIDE 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Purity  of  Sodium  Chloride.  Sodium  chloride  which  contains 
the  theoretical  percentage  of  chlorine  can  be  obtained  from  dealers. 
Impure  samples  can  be  easily  purified  by  preparing  a  nearly  sat- 
urated solution,  and  passing  a  stream  of  hydrochloric  acid  gas  into 
it  until  a  sufficient  amount  of  the  salt  precipitates,  which  is  then 
separated  on  a  Witt  filter-plate  and  dried.  It  is  not  sufficiently 
hygroscopic  to  make  accurate  weighing  difficult,  but  samples, 
which  have  stood  in  a  moist  atmosphere  for  some  time  may  contain 
one  per  cent  of  water.  $44*4**?^ 

Properties  of  Silver  Chloride.  When  first  precipitated  silver 
chloride  is  very  finely  divided  and  is  then  retained  on  a  filter  with 
some  difficulty,  if,  however,  the  solution  is  slightly  acid,  and  if 
kept  hot  and  stirred  vigorously,  or  if  allowed  to  stand  for  several 
hours  the  fine  particles  gradually  coalesce,  and,  owing  to  their 
high  specific  gravity,  rapidly  settle  to  the  bottom  of  the  containing 
vessel.  A  solution  of  silver  nitrate  containing  24  gm.  of  the 
crystallized  salt  per  liter  forms  a  convenient  reagent  for  the 
precipitation  of  chlorine;  1  cc.  of  such  a  solution  should  precipitate 
0.005  gm.  of  chlorine. 

The  solubility  of  silver  chloride  is  extremely  small;  it  is  increased 
by  the  presence  of  large  concentrations  of  nitric  and  hydrochloric 
acid  and  the  chlorides  and  nitrates  of  ammonium  and  the  alkali 
metals.  When  digested  with  pure  water  it  slowly  changes  into 
a  colloidal  form,  but  this  change  is  prevented  by  the  presence  of 
a  small  amount  of  nitric  acid  or  any  other  soluble  electrolyte.  v 

150 


DETERMINATION  OF  CHLORINE  IN  SODIUM  CHLORIDE      151 


When  freshly  precipitated  silver  chloride  is  exposed  to  strong 
sunlight  it  darkens;  this  change  is  associated  with  the  formation 
of  a  subchloride  and  the  liberation  of  chlorine.  Since  the  precipi- 
tate is  not  transparent  the  action  is  superficial  only,  and  the 
percentage  acted  upon  is  small  unless  the  mass  of  precipitate  is 
continually  broken  up  by  stirring. 

Pure  silver  chloride  fuses  at  460°  without  change  of  composition 
and  produces  a  yellow  viscous  liquid,  which  forms  a  tough,  horny 
mass  when  allowed  to  solidify.  It  begins  to 
volatilize  at  about  the  same  temperature,  and 
appreciable  amounts  may  be  driven  off  if  the 
heating  is  continued  for  some  minutes. 

Like  most  of  the  compounds  of  silver  this 
precipitate  is  easily  reduced  to  the  metal  by 
even  weak  reducing  agents.  The  efficiency 
of  organic  matter  as  a  reducing  agent  makes 
it  necessary  to  use  extreme  care  in  igniting 
the  precipitate  when  separated  on  a  paper 
filter,  and  renders  the  use  of  an  asbestos  filter 
preferable.  '* 


Fig.  39.  — Wash 
Bottle 


II.   PREPARATION  OF  A  WASH  BOTTLE 

This  determination  requires  the  use  of  an 
efficient  and  convenient  "wash  bottle/7  similar 
to  the  one  represented  in  Fig.  39.  It  should 
be  provided  with  a  flexible  joint  at  A  and  two  or  more  easily 
detachable  nozzles,  which  can  be  used  to  produce  streams  of 
varying  size.  The  delivery  tube  should  be  bent  at  B  in  order 
to  permit  of  a  more  complete  expulsion  of  the  water  when  the 
flask  is  held  in  an  inclined  position. 

III.   OUTLINE  OF  METHOI>  OF  PROCEDURE 

Weighing  Out  the  Sample.     Place  about  3  gm.  of  the  salt  in 
a  porcelain  or  platinum  crucible,  cover  and  heat  gradually  with 


152  QUANTITATIVE  CHEMICAL  ANALYSIS 

a  burner  until  the  salt  no  longer  decrepitates.  Allow  the  crucible 
to  cool  somewhat,  but  while  still  warm  pour  the  salt  into  a  clean, 
well-stoppered  sample  tube;  when  the  tube  has  assumed  the  tem- 
perature of  the  balance-room  weigh  accurately  to  a  tenth  of  a 
milligram.  Hold  the  tube  over  a  clean  250  cc.  beaker,  remove 
the  stopper  and  carefully  pour  into  the  beaker  from  0.2  to  0.4  gm. 
(not  more)  of  the  sample,  then  replace  the  stopper  and  again  weigh 
accurately. 

Preparation  of  Solution  and  Precipitation.  Dissolve  the 
sample  in  about  100  cc.  of  water,  add  1  cc.  of  dilute  nitric  acid  and 
then  slowly  and  with  constant  stirring  a  slight  excess  of  silver 
nitrate  solution;  5  cc.  of  the  reagent  referred  to  above  in  excess  of 
the  amount  theoretically  required  is  sufficient.  Next  heat  the 
solution  gradually  to  the  boiling  point,  and  keep  somewhat  below 
this  temperature,  stirring  -  continuously,  until  the  precipitate 
coagulates  and  the  supernatant  liquid  is  clear;  or  allow  the  beaker 
to  stand  for  several  hours  after  heating  to  the  boiling  point.  The 
beaker  should  be  kept  away  from  direct  sunlight  as  much  as 
possible. 

Filtration  and  Ignition  of  Precipitate.  Connect  a  clean  Gooch 
crucible  with  a  suction  flask  as  shown  in  Fig.  29.  Attach  the  flask 
to  the  suction  pump  and  add  to  the  crucible  sufficient  asbestos 
pulp  to  leave  a  compact  layer  about  2  mm.  thick  when  drawn 
against  the  bottom  of  the  crucible  by  means  of  the  pump  and 
place  a  thin  Witt  filter  plate  on  top  of  the  asbestos.  Pass 
100  cc.  or  more  of  water  thru  the  filter  till  all  loosely  adhering 
fibers  are  rinsed  from  the  outside  of  the  crucible.  Remove  the 
crucible  from  the  filter  tube,  place  in  a  muffle  and  heat  for  about 
twenty  minutes  at  a  temperature  of  200°.  Cool  in  a  desiccator 
and  then  weigh  accurately. 

Clean  and  rinse  out  the  suction  flask,  connect  the  crucible  with 
it  as  before,  start  the  suction  pump  and  decant  the  solution  from 
the  silver  precipitate  thru  the  crucible.  Add  to  the  precipitate 
in  the  beaker  about  25  cc.  of  water,  stir  the  mixture  for  a  few 


DETERMINATION  OF  CHLORINE  IN  SODIUM  CHLORIDE      153 

minutes,  then  allow  it  to  settle  and  again  decant  thru  the  filter. 
Wash  with  three  more  25  cc.  portions  of  water,  to  each  of  which 
about  one  half  cc.  of  dilute  nitric  acid  has  been  added.  Transfer 
the  precipitate  from  the  beaker  to  the  filter  by  means  of  a  stream 
of  water  from  the  wash  bottle  directed  back  of  the  precipitate. 
Finally  loosen  all  particles  of  precipitate  which  adhere  to  the 
surface  of  the  beaker  by  means  of  a  rubber-tipped  rod  and  rinse 
these  also  into  the  filter.  Test  the  last  washings  for  soluble  silver 
salts  by  removing  20  cc.  and  adding  a  drop  of  dilute  hydrochloric 
acid.  If  this  test  shows  an  appreciable  turbidity  continue  washing 
with  water  containing  a  little  nitric  acid  until  another  test  shows 
that  the  silver  salts  have  been  removed.  Finally  wash  with  10  cc. 
of  pure  water. 

Place  the  crucible  in  a  muffle,  heat  slowly  to  200°  and  keep  at 
that  temperature  for  twenty  minutes,  then  allow  it  to  cool  in  a 
desiccator  and  weigh  accurately.  Again  heat  for  ten  minutes  and 
reweigh  and  if  necessary  continue  heating  and  weighing  until  two 
consecutive  weighings  do  not  differ  by  more  than  3  mg.  Calculate 
and  report  the  percentage  of  chlorine  found. 


IV.   QUESTIONS  AND  PROBLEMS.    SERIES  6 

-  1.  If  you  were  required  to  determine  the  percentage  of  iodine  in  sodium 
iodide  by  precipitating  as  silver  iodide,  would  it  be  desirable  to  either  increase 
or  decrease  the  amount  of  sample  used,  as  compared  with  the  amount  used  in 
this  determination? 

2.  Could  any  other  acid  than  nitric  be  used  to  acidify  the  solution  before 
precipitating  silver  chloride? 

3.  If  so  much  of  the  precipitate  was  reduced  that  one-fourth  of  the  pre- 
cipitate actually  weighed  consisted  of  Ag2Cl,  how  large  a  departure  from  the 
correct  result  would  appear  in  the  report? 

4.  Calculate  the  weight  of  silver  chloride  dissolved  by  1  liter  of  a  solution 
which  contained  1  gm.  of  hydrochloric  acid,  assuming  that  the  solubility  prod- 
uct of  silver  chloride  is  constant  and  that  it  and  the  hydrochloric  acid  are 
completely  dissociated. 


154  QUANTITATIVE  CHEMICAL  ANALYSIS 

,  6.  If  you  added  silver  nitrate  very  slowly  to  a  solution  which  had  a  volume 
of  100  cc.  and  contained  0.1  gm.  of  KCNS  and  0.1 /gm.  of  KC1,  what  changes 
would  take  place? 

6.  If  the  silver  nitrate  solution  used  in  this  determination  had  contained  a 
small  amount  of  lead  nitrate,  would  you  expect  it  to  affect  the  result? 

7.  How  would  you  utilize  the  silver  precipitates  obtained  in  these  deter- 
minations for  the  preparation  of  silver  nitrate  reagent? 


CHAPTER  XXI 

DETERMINATION   OF  MAGNESIUM  IN  MAGNESIUM  SULFATE 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Outline  of  Method.  The  magnesium  ion  is  precipitated  by 
neutral  or  alkaline  solutions  of  soluble  phosphates,  but  the  resulting 
precipitates  may  consist  of  mixtures  of  di-  and  tribasic  phosphates, 
or  of  a  number  of  double  phosphates.  Under  certain  conditions 
a  pure  precipitate  of  Mg(NH4)P04-6  H20  can  be  obtained,  and 
since  this  precipitate  is  converted  into  Mg2P207  by  ignition,  mag- 
nesium is  usually  determined  in  this  form. 

Solubility  of  the  Precipitate.  The  solubility  of  this  precipi- 
tate is  greater  than  that  of  most  precipitates  used;  it  cannot  be 
accurately  determined  owing  to  a  partial  decomposition  in  pure 
water,  which  is  represented  by  the  expression 

Mg(NH4)P04  •  6  H20  -»  MgHP04  +  (NH4)HO  +  5  H20. 

This  reaction  is  reversed  by  the  presence  of  moderate  concen- 
trations of  ammonium  hydroxide,  and  an  excess  of  this  reagent 
must  be  used  in  making  the  precipitation  and  in  washing  the 
precipitate. 

Conditions  Necessary  for  Precipitation.  A  solution  of 
Na2HP04  •  12  H20  containing  44.75  gm.  per  liter,  which  is  equiva- 
lent to  0.005  gm.  of  Mg  per  cc.,  is  a  convenient  reagent  to  use  for 
this  precipitation.  Experience  shows  that  unless  one  and  one-half 
times  the  theoretically  required  amount  of  reagent  is  used  low 
results  are  obtained.  This  has  been  attributed  to  the  formation 
of  small  amounts  of  Mg3(P04)2.  It  has  also  been  shown  that  if 
the  solution  contains  very  large  concentrations  of  NH4  ions,  high 

155 


15G  QUANTITATIVE  CHEMICAL   ANALYSIS 

results  are  obtained.  This  has  been  attributed  to  the  formation 
of  small  amounts  of  (NH4)4Mg(P04)2  which  yields  Mg(PO3)2  on 
ignition.  The  concentration  of  the  NH4  ions  depends  for  the 
most  part  upon  the  concentration  of  the  ammonium  salts  present, 
but  in  part  upon  the  concentration  of  ammonium  hydroxide. 

Several  chemists  have  formulated  the  exact  conditions  neces- 
sary to  effect  complete  separation  of  magnesium  in  the  desired 
form;  the  method  devised  by  Gooch  and  Austin*  will  be  used 
here.  In  this  method  the  proper  excess  of  sodium  phosphate  is 
first  added  to  the  neutral  or  slightly  alkaline  solution,  which 
produces  a  precipitate  assumed  to  contain  small  amounts  of 
Mg3(P04)2.  This  precipitate  is  redissolved  by  adding  a  few  drops 
of  dilute  hydrochloric  acid  and  the  magnesium  reprecipitated  by 
the  very  gradual  addition  of  dilute  ammonium  hydroxide.  Suffi- 
cient soluble  phosphate  is  present  during  the  second  precipitation 
to  prevent  the  formation  of  Mg3(PO4)2,  and  an  undesirably  large 
concentration  of  (NH4)  ions  is  avoided. 

The  precipitate  obtained  should  be  coarsely  crystalline;  it  shows 
some  tendency  for  the  formation  of  supersaturated  solutions,  but 
under  ideal  conditions  complete  separation  should  take  place 
within  a  half  hour.  The  separation  is  retarded  by  the  presence 
of  large  concentrations  of  ammonium  salts,  and  it  is  sometimes 
necessary  to  allow  the  mixture  to  stand  for  twelve  hours  or  to  stir 
vigorously  for  an  hour. 

Conditions  Necessary  for  Ignition.  A  very  high  temperature 
must  be  used  to  convert  Mg(NH4)P04  into  Mg2P207,  hence  the 
precipitate  should  be  ignited  in  a  small  crucible  with  a  Meker  or 
Chaddock  burner,  or  over  a  blast  lamp.  At  the  temperature 
finally  attained  a  slight  sintering  of  the  precipitate  takes  place, 
and  if  particles  of  unconsumed  filter  paper  are  still  present  they 
may  be  so  surrounded  as  to  prevent  complete  oxidation.  Hence 
the  temperature  should  be  kept  rather  low  until  the  combustible 
matter  has  been  consumed.  This  difficulty  can  usually  be  avoided 
*  Zeit.  fur  anorganische  Chemie,  20,  121  (1899). 


MAGNESIUM  IN  MAGNESIUM  SULFATE  157 

by  moistening  the  precipitate  and  filter  with  a  few  drops  of  a 
strong  solution  of  ammonium  nitrate  before  ignition. 

Some  chemists  prefer  to  separate  this  precipitate  on  a  Gooch 
crucible,  but  the  large  size  of  these  crucibles  increases  the  difficulty 
of  bringing  the  precipitate  to  the  proper  temperature.  Altho  the 
precipitate  is  not  readily  reduced,  it  is  not  wise  to  ignite  it  in  a 
platinum  crucible  as  the  latter  becomes  brittle  and  soon  cracks  if 
used  repeatedly  for  this  purpose;  this  is  probably  due  to  the  forma- 
tion of  a  small  amount  of  a  phosphide  of  platinum. 

II.   OUTLINE  OF  THE  METHOD  OF  PROCEDURE 

Weighing  Out  and  Precipitating  the  Sample.  Place  3  to  4  gm.  \ 
of  the  pure  dry  salt  in  a  clean  sample  tube  and  weigh  out  about  \ 
I  gm.  into  a  200  cc.  beaker.  Dissolve  the  sample  in  about  50  cc. 
of  water,  add  one  and  one-half  times  the  theoretically  required 
volume  of  sodium  phosphate  solution,  and  then  add  dilute  hydro- 
chloric acid  drop  by  drop  until  the  precipitate  which  has  separated 
redissolves.  Dilute  in  a  separate  vessel  10  cc.  of  dilute  ammonium 
hydroxide  to  50  cc.,  and  add  this  solution  drop  by  drop  with  con- 
stant stirring  until  the  solution  when  tested  with  a  narrow  piece 
of  red  litmus  paper  shows  a  slight  alkaline  reaction.  Next  add 
slowly  20  cc.  of  dilute  ammonium  hydroxide  and  allow  the  mix- 
ture to  stand,  stirring  it  occasionally,  for  one-half  hour. 

Filtration.  Fold  a  9  cm.  ashless  filter  paper  to  accurately  fit  a 
funnel  of  slightly  larger  size  and  moisten  with  water.  Decant 
the  clear  portion  of  the  solution  thru  the  filter,  then  transfer  the 
precipitate  to  it  by  means  of  a  stream  from  a  wash  bottle  which 
contains  a  mixture  of  one  volume  of  dilute  ammonium  hydroxide 
to  four  of  water.  Continue  washing  with  this  mixture  until 
20  cc.  of  the  washings  give  no  recognizable  test  for  chlorine. 
Finally  moisten  the  precipitate  and  filter  with  a  few  drops  of  a 
five  per  cent  solution  of  ammonium  nitrate. 

Igniting  and  Weighing  the  Precipitate.  Dry  the  filter  and 
while  waiting  for  it  to  dry  ignite  and  weigh  a  small  porcelain 


158  QUANTITATIVE  CHEMICAL  ANALYSIS 

crucible.  Separate  the  precipitate  as  far  as  possible  from  the 
filter  and  set  aside  on  a  watch  glass;  roll  the  filter  into  a  ball,  place 
in  the  crucible  and  heat  the  latter  over  a  gauze  until  the  paper  is 
consumed.  Next  add  the  main  portion  of  the  precipitate  and 
ignite  gently  at  first,  but  finally  with  the  full  heat  of  a  Meker  or 
Chaddock  burner  for  about  twenty  minutes.  If  the  precipitate 
does  not  become  white  at  the  end  of  this  time  allow  it  to  cool,  moisten 
with  a  few  drops  of  strong  nitric  acid,  evaporate  off  the  acid  and 
again  ignite.  Allow  to  cool,  then  weigh  and  repeat  the  ignition 
until  successive  weighings  do  not  differ  by  more  than  .3  mg.  Cal- 
culate and  report  the  percentage  of  Mg  present. 

III.   QUESTIONS  AND  PROBLEMS.    SERIES  7 

1.  Write  out  all  of  the  reactions  concerned  in  the  determination. 

2.  What  reagents  should,  according  to  the  general  theory  of  precipitation 
of  electrolytes,  reduce  the  solubility  of  Mg(NH4)PO4;   which  of  these  could 
be  used  in  the  determination  of  magnesium? 

3.  If  you  were  to  weigh  out  1  gm.  of  a  sample,  which  contained  0.1  gm.  of 
Mg.,  and  the  precipitate  obtained  contained  in  one  case  0.01  gm.  of  Mg3(PO4)2 
and  in  the  other  0.01  gm.  of  Mg(PQ4)2,  what  percentages  would  be  reported 
if  it  was  assumed  that  all  of  the  precipitate  was  Mg2P2O7? 

4.  Is  there  any  objection  to  neutralizing  the  solution  with  sodium  or  po- 
tassium hydroxide  rather  than  ammonium  hydroxide,  to  dissolving  the  pre- 
cipitate first  obtained  in  H2SO4  or  HNO3  rather  than  HC1,  to  washing  the 
precipitate  with  potassium  hydroxide? 

6.   What  is  the  probable  formula  of  a  salt  which  contains  5.97  per  cent  Mg, 
19.40  per  cent  K,  47.76  per  cent  SO4,  26.86  per  cent  H2O? 


CHAPTER  XXII 

DETERMINATION  OF  IRON  IN  FERROUS  AMMONIUM  SULFATE  BY 
THE   USE   OF  THE   ELECTRIC   CURRENT 

I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Composition  of  Ferrous  Ammonium  Sulfate.  This  salt  has 
the  formula  FeS04  •  (NH4)2S04  •  6  H20  and  is  readily  obtained  in  a 
'  high  degree  of  purity.  As  it  slowly  oxidizes  and  loses  some  of  its 
water,  even  at  25°,  it  should  be  preserved  in  a  stoppered  bottle  in 
a  cool  place.  If  these  changes  have  taken  place  the  crystals  show 
a  reddish  color  and  lack  their  usual  transparency. 

Conditions  Necessary  for  the  Separation.  The  decomposi- 
tion voltage  of  the  ferrous  ion  is  0.34  volt  higher  than  that  of  the 
hydrogen  ion  and  the  metal  cannot  be  separated  from  solutions  by 
an  electric  current  unless  the  concentration  of  the  hydrogen  ion 
is  small.  It  is  not  possible  to  separate  the  metal  in  a  satisfactory 
form  from  solutions  of  simple  ferrous  salts,  but  good  results  are 
obtained  if  the  solution  also  contains  a  large  concentration  of 
ammonium  or  potassium  oxalate. 

The  solubility  of  ferrous  oxalate  is  only  0.077  gm.  per  liter,  and 
since  double  oxalates  of  ammonium  and  potassium  are  easily  pre- 
pared, it  is  probable  that  most  of  the  iron  in  such  solutions  is  in 
the  form  of  a  complex  ion.  The  composition  of  this  ion  is  not 
definitely  known,  but  its  formation  can  be  represented  by 

x  FeC204  +  y  C26,  +  2  ?/(NH4)  ->  (FeC204],(C204)2/  +  2  ?/(NH4). 

It  has  been  shown  that  for  every  atom  of  iron  present  in  such 
solutions  four  molecules  of  potassium  oxalate  must  be  present  to 
prevent  the  separation  of  a  precipitate  containing  iron.  Such 
precipitates  are  not  easily  dissolved  by  the  addition  of  further 

159 


160  QUANTITATIVE  CHEMICAL  ANALYSIS 

amounts  of  soluble  oxalates,  and  in  preparing  the  solution  care 
must  be  taken  to  add  the  iron  solution  to  a  concentrated  solution 
of  the  soluble  oxalate.  The  voltage  necessary  for  the  separation 
of  iron  from  such  solutions  is  somewhat  higher  than  that  necessary 
to  separate  it  from  solutions  of  simpler  composition. 

Secondary  Effects  of  the  Electrolysis.  The  C204  ions  present 
are  slowly  oxidized  to  C03^ons  at  the  anode  and  since  the  tem- 
perature of  the  solution  may  rise  to  60°,  owing  to  the  large  amper- 
ages usually  employed,  much  carbon  dioxide  is  expelled.  As 
NH3  is  not  expelled  to  the  same  extent,  the  solution  may  acquire 
a  sufficient  degree  of  alkalinity  to  precipitate  some  of  the  iron; 
it  then  becomes  necessary  to  add  sufficient  oxalic  acid  to  dissolve 
the  precipitate. 

Properties  of  the  Precipitate.  The  separated  metal  forms 
smooth  coherent  deposits  even  when  deposited  on  foil  electrodes, 
by  the  use  of  a  current  measuring  as  much  as  three  amperes 
(normal  density).  It  is  not  acted  upon  appreciably  by  the  solution 
as  usually  prepared,  but  is  rapidly  dissolved  by  even  small  concen- 
trations of  mineral  acids.  It  is  easily  oxidized,  especially  when 
moist,  and  must  be  rinsed  with  at  least  two  changes  of  alcohol  to 
displace  the  adhering  water,  dried  at  a  temperature  not  in  excess 
of  60°,  and  weighed  without  delay,  if  oxidation  is  to  be  avoided. 

Effect  of  Additional  Substances.  Solutions  containing  ferric 
sulfate  or  chloride  also  form  double  oxalates,  but  since  reduction 
to  the  ferrous  condition  precedes  precipitation  of  the  metal  the 
time  needed  is  greater.  The  presence  of  the  N03  ion  must  be 
avoided,  owing  to  its  oxidizing  power.  The  presence  of  all  metals 
which  stand  below,  or  only  slightly  above  iron  in  the  electro- 
potential  series  must  be  avoided. 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 
Splitting  a  Watch  Glass.     The  large  amount  of  gas  liberated 
during  this  electrolysis  makes  it  necessary  to  cover  the  containing 
vessel;  a  watch  glass  which  has  been  split  into  halves  can  be  used 


IRON   IN   FERROUS  AMMONIUM   SULFATE  161 

with  advantage.  To  split  the  glass  make  a  scratch  on  its  convex 
surface  with  a  steel  or  diamond  glass-cutter,  using  a  piece  of  card- 
board for  a  straight  edge,  and  then  bring  the  glass  along  the 
scratched  line  into  contact  with  a  piece  of  fine  nichrome  wire  which 
is  heated  to  dull  redness  by  means  of  an  electric  current.  If  the 
glass  does  not  fall  apart  at  once  place  a  drop  of  cold  water  on  the 
line  heated  by  the  wire. 

Preparation  of  the  Solution.  Place  about  5  gm.  of  the  salt  in 
a  dry  sample  tube  and  weigh  out  about  1  gm.  into  a  100  cc.  beaker. 
Add  25  cc.  of  water  and  stir  until  the  salt  dissolves.  Weigh  out 
approximately  6  gm.  of  crystallized  ammonium  oxalate  into  a 
200  cc.  beaker  of  narrow  form,  add  50  cc.  of  water,  warm  and  stir 
till  the  salt  dissolves.  Add  the  iron  solution  to  the  oxalate  solu- 
tion, and  rinse  out  the  beaker  with  three  10  cc.  portions  of  water. 
The  resulting  mixture  should  be  perfectly  clear  and  of  a  deep 
yellow  color. 

Electrolysis  of  the  Solution.  Ignite  a  clean  platinum  cathode 
of  the  Mansfeld  or  Winkler  type  in  the  flame  of  a  burner,  allow 
to  cool  without  placing  in  a  desiccator,  and  weigh  accurately. 
Place  the  cathode  in  the  iron  solutions  and  an  anode  in  the  center 
of  the  cathode  cylinder.  Carry  the  beaker  to  the  bench  contain- 
ing an  installation  similar  to  that  represented  in  Fig.  38.  Throw 
the  ammeter  and  voltmeter  switches  opposite  one  of  the  vacant 
electrolytic  stands  to  the  point  marked  zero,  and  turn  the  arm  of 
the  adjustable  rheostat  well  over  to  the  left  of  the  center  as  shown 
in  the  figure.  Connect  the  cathode  with  the  lower  arm  of  the 
electrolytic  stand  and  the  anode  with  the  upper  arm,  carefully 
adjusting  both  electrodes  so  that  both  extend  to  within  a  few  mm. 
of  the  bottom  of  the  beaker,  but  do  not  come  into  contact  with 
one  another. 

Next  note  whether  the  needle  of  the  ammeter  (the  one  reading  up 
to  fifteen  amperes)  stands  at  zero,  which  means  that  the  instrument 
is  not  being  used  on  any  of  the  other  circuits,  and  if  not  at  zero 
wait  until  out  of  use.  As  soon  as  the  pointer  of  the  instrument 


162  QUANTITATIVE  CHEMICAL  ANALYSIS 

stands  at  zero  throw  the  ammeter  switch  to  the  point  marked  two 
and  slowly  turn  the  arm  of  the  rheostat  till  the  instrument  shows 
that  a  current  of  one  and  one-half  amperes  is  flowing  thru  the  circuit  ; 
then  throw  the  ammeter  switch  back  to  the  point  marked  one. 
Next  turn  the  voltmeter  switch  to  the  point  nearest  the  circuit 
in  use  and  after  recording  the  reading  of  the  needle  return  the 
switch  to  the  central  point. 

Allow  the  current  to  run  for  80  minutes  if  the  Winkler  cathode 
is  used,  or  two  hours  if  a  Mansfeld  cathode  is  used.  At  the  end 
of  this  time  the  solution  should  be  perfectly  colorless  and  should 
show  no  traces  of  precipitate. 

Washing  and  Weighing  the  Cathode.  Fill  a  200  cc.  beaker 
with  distilled  water  and  place  on  the  desk  near  the  solution;  raise 
the  electrolytic  stand  without  breaking  the  circuit  or  disconnecting 
the  attached  wires  and  plunge  the  electrodes  without  loss  of  time 
into  the  beaker  of  water.  Add  to  the  beaker  containing  the 
residual  solution  a  few  cc.  of  potassium  ferrocyanide;  if  it  gives 
a  perceptible  reaction  for  iron  the  determination  should  be 
repeated.  If  no  iron  is  found  in  the  solution,  disconnect  the 
cathode  and  rinse  in  the  water  of  the  beaker,  then  remove  and 
bring  into  contact  with  a  large  piece  of  filter  paper  until  most  of  the 
adhering  water  has  been  absorbed.  Rinse  the  cathode  in  alcohol, 
using  first  the  cylinder  marked  "for  first  washing"  then  the 
cylinder  marked  "for  second  washing,"  which  should  contain 
98  per  cent  alcohol,  and  drain  on  a  piece  of  filter  paper.  Dry  in 
an  air  bath  at  a  temperature  of  about  60°.  Do  not  allow  the 
alcohol  on  the  cathode  to  catch  fire;  if  it  does  so  the  precipitated 
iron  will  also  burn,  and  the  heat  liberated  will  cause  some  of  it  to 
alloy  with  the  platinum  and  spoil  the  electrode.  Weigh  the 
electrode  accurately  and  calculate  the  per  cent  of  iron  present. 
Place  the  cathode  in  a  beaker  containing  dilute  sulfuric  acid  and 
allow  it  to  remain  until  absolutely  all  the  deposited  iron  has  been 
dissolved  off;  this  can  be  determined  by  noting  whether  hydrogen 
is  liberated. 


IRON  IN  FERROUS  AMMONIUM   SULFATE  163 

III.   QUESTIONS  AND  PROBLEMS.     SERIES  No.  8 

1.  Explain  why  a  large  amount  of  gas  is  liberated  at  the  cathode  during 
the  later  stages  of  the  deposition  but  not  during  the  earlier. 

2.  On  the  basis  of  Faraday's  law  how  long  a  time  would  be  required  to 
deposit  all  the  iron  present  under  the  conditions  used?     Why  is  the  calcu- 
lation of  no  practical  value? 

3.  Exactly  why  is  the  formation  of  a  precipitate  prevented  by  adding  the 
iron  solution  to  the  oxalate  solution? 

4.  If  the  ferrocyanide  test  used  showed  that  iron  was  still  present  why  not 
replace  the  electrodes  in  the  solution  and  continue  the  electrolysis  instead 
of  discarding  the  determination? 

6.  If  the  decomposition  voltage  of  a  normal  solution  of  the  ferrous  ion  is 
+0.34  volt,  what  voltage  would  it  be  necessary  to  use  to  reduce  the  concen- 
tration of  the  ferrous  ions  to  0.0001  gm.  in  a  volume  of  100  cc.? 

6.  Outline  an  electrolytic  method  for  the  determination  of  iron  in  a  sample 
of  iron  wire  and  give  all  the  reactions  concerned. 

7.  How  many  storage  battery  cells,!  each  of  which  is  capable  of  furnishing 
2.2  volts,  would  be  necessary  to  make  ten  determinations  of  iron  at  once, 
assuming  that  one  ampere  is  used,  that  the  resistance  of  each  solution  and  its 
connections  is  0.5  ohm^nd  that  the  cells  are  arranged  in  parallel? 

8.  What  difference  would  it  make  if  the  solutions  in  the  above  problem 
were  connected  in  series? 


CHAPTER  XXIII 

DETERMINATION   OF   SULFUR  IN  IRON  PYRITES 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Composition  of  Pyrites.  This  mineral  is  represented  by  the 
formula  FeS2,  but  it  is  frequently  associated  with  the  sulfides  of 
other  metals,  especially  copper,  zinc,  arsenic  and  lead,  with  the 
sulfates  of  calcium  and  barium,  and  almost  invariably  with  silica 
and  various  insoluble  silicates.  It  is  assumed  that  the  sample 
used  for  this  determination  contains  at  least  35  per  cent  of  sulfur, 
only  small  amounts  of  copper,  zinc  and  arsenic,  and  neither  barium 
nor  lead.  It  is  assumed  further  that  the  sample  has  been  crushed 
and  passed  thru  a  sixty-mesh  sieve,  carefully  mixed  and  dried. 

Methods  of  Oxidizing  Sulfides.  Two  methods  are  in  general 
use  for  the  oxidation  of  naturally-occurring  sulfides;  in  one  the 
mineral  is  treated  with  a  strong  mineral  acid  and  a  strong  oxidizing 
agent,  such  as  potassium  chlorate,  nitric  acid  or  brcmine;  in  the 
other  it  is  fused  with  a  mixture  of  sodium  carbonate  and  either 
sodium  peroxide  or  potassium  nitrate.  The  presence  of  N03  ions 
in  the  solution  from  which  barium  sulfate  is  to  be  precipitated 
must  be  avoided,  owing,  as  shown  on  page  131,  to  the  extent  to 
which  nitrates  are  occluded.  Since,  however,  the  N03,  C1O3  and 
Br  ions  can  be  easily  expelled  by  evaporating  the  solution  with  a 
large  excess  of  hydrochloric  acid,  and  since  no  sulfuric  acid  is 
expelled  if  this  evaporation  is  made  on  a  steam  bath,  there  is  no 
objection  to  the  method  of  oxidation  first  named.  The  presence 
of  the  large  amounts  of  sodium  and  potassium  salts  necessarily 
introduced  in  oxidizing  by  the  fusion  process  also  results  in  errors 
from  occlusion,  and  since  these  salts  cannot  be  removed  from  the 

164 


DETERMINATION  OF  SULFUR   IN   IRON  PYRITES       165 

solution  by  any  satisfactory  process  this  method  of  oxidation  is  to 
be  avoided. 

Most  samples  of  pyrites  can  be  completely  and  rapidly  oxidized 
by  means  of  a  mixture  of  three  volumes  of  concentrated  nitric 
and  one  of  concentrated  hydrochloric  acid.  In  some  instances, 
especially  where  the  temperature  of  the  mixture  is  allowed  to  rise 
too  high,  and  the  decomposition  of  the  sample  takes  place  too 
rapidly,  small  amounts  of  free  sulfur  may  separate;  this  can 
usually  be  oxidized  by  the  addition  of  a  few  drops  of  liquid  bromine, 
whose  oxidizing  properties  are  stronger  than  those  of  nitric  acid. 
Treatment  of  the  sample  with  this  mixture  and  the  subsequent 
evaporation  with  hydrochloric  acid  insures  complete  oxidation  of 
the  iron  and  arsenic,  and  renders  all  constituents  soluble  except 
silica  and  the  insoluble  silicates. 

Separation  of  the  Iron  Before  Precipitation  of  Barium  Sulfate. 
The  filtrate  from  the  insoluble  matter  will  contain  large  amounts 
of  ferric  chloride,  also  the  chlorides  of  the  other  metals  present. 
If  barium  sulfate  is  precipitated  from  such  a  solution  it  will  contain 
occluded  ferric  sulfate  and,  as  shown  on  page  130,  this  will  lead  to 
very  low  results. 

If  the  iron  is  precipitated  by  the  addition  of  ammonium  hy- 
droxide, appreciable  amounts  of  ammonium  salts  are  added  to  the 
solution,  and  as  ammonium  sulfate  is  both  occluded  by  the  preci- 
pitate and  expelled  during  ignition,  a  rather  large  error  may  result 
unless  the  amount  of  acid  present  in  the  solution  before  precipita- 
tion is  reduced  to  a  minimum. 

The  precipitate  obtained  by  the  addition  of  ammonium  hy- 
droxide to  a  solution  containing  ferric  sulfate  may  contain  appreci- 
able amounts  of  basic  sulfates,  unless  a  relatively  large  excess  of 
precipitant  is  used  and  the  mixture  heated  for  some  time.  Even 
when  no  basic  sulfates  have  been  formed,  it  is  difficult  to  wash  out 
the  last  traces  of  soluble  sulfates  from  the  precipitate,  and  it  is 
not  safe  to  discard  the  latter  until  it  has  been  proved  to  be  free 
from  these  compounds.  The  washed  precipitate  can  be  dissolved 


166  QUANTITATIVE  CHEMICAL  ANALYSIS 

in  a  very  small  amount  of  warm  dilute  hydrochloric  acid,  the  iron 
again  separated  and  the  sulfur  precipitated  in  the  resulting  nitrate. 
Under  the  proper  conditions  the  weight  of  barium  sulfate  obtained 
from  the  second  filtrate  should  not  exceed  10  mg.,  and  is  often 
inappreciable.  Where  extreme  accuracy  is  not  essential  the 
method  may  be  abbreviated  somewhat  by  precipitating  the  small 
amount  of  barium  sulfate  in  the  hydrochloric  acid  solution  of  the 
precipitate,  without  removing  the  iron. 

Properties  of  Barium  Sulfate.  The  solubility  of  barium  sul- 
fate amounts  to  2.2  mg.  per  liter;  it  is  increased  by  small  concen- 
trations of  nitric  or  hydrochloric  acid;  it  is  decreased  by  small 
concentrations  of  sulfuric  acid  or  salts  which  yield  SO4  ions,  but 
the  salt  is  decidedly  soluble  in  concentrated  sulfuric  acid.  It  has 
a  density  of  4.49  gm.,  and  when  precipitated  under  the  proper 
conditions  settles  rapidly.  As  much  as  2  gm.  of  the  precipitate 
can  be  easily  and  rapidly  filtered  and  washed  on  an  11  cm.  filter. 

The  barium  sulfate  precipitate  is  usually  classed  as  pulverulent, 
but  its  properties  are  affected  to  a  large  extent  by  the  conditions 
of  precipitation.  That  produced  by  the  addition  of  a  salt  of 
barium  to  a  cold  concentrated  solution  of  a  soluble  sulfate  is  often 
so  finely  divided  that  it  cannot  be  retained  on  the  filters  usually 
employed.  Altho  long-continued  digestion  increases  the  size  of  the 
particles  of  which  such  a  precipitate  is  composed,  it  is  preferable 
to  avoid  the  formation  of  such  precipitates  by  causing  it  to  separate 
from  a  hot  solution  whose  concentration  does  not  exceed  3  gm.  of 
S04  per  liter.  The  presence  of  a  small  amount  of  acid  makes  the 
precipitate  more  compact,  causes  it  to  settle  more  rapidly,  and 
reduces  its  tendency  to  creep. 

The  conditions  which  result  in  the  formation  of  a  precipitate  of 
the  most  desirable  physical  properties  also  result  in  a  slight 
tendency  for  supersatu ration.  Under  the  conditions  which  are 
recommended  later  the  precipitate  should  be  allowed  to  stand  for 
at  least  two  hours  before  filtration;  increasing  the  amount  of  acid 
increases  the  time  necessary  for  complete  separation. 


DETERMINATION  OF  SULFUR  IN   IRON  PYRITES       167 

The  precipitate  produced  by  the  addition  of  a  salt  of  barium  to 
a  slightly  alkaline,  or  even  to  a  neutral  solution  of  a  soluble  sulfate 
may  contain,  in  addition  to  barium  sulfate,  small  amounts  of  basic 
sulfates,  and,  also,  as  the  result  of  the  absorption  of  carbon  dioxide 
from  air,  of  barium  carbonate.  The  presence  of  a  slight  concen- 
tration of  hydrogen  ions  prevents  the  formation  of  either  of  these 
compounds.  If,  however,  the  concentration  of  the  hydrogen  ions 
is  not  kept  very  small,  low  results  are  obtained,  owing  to  the  fact 
that  under  these  conditions  appreciable  amounts  of  an  acid  sulfate 
of  barium  is  occluded.  The  maximum  concentration  of  hydrogen 
ions  should  not  exceed  0.02  gm.  per  liter. 

Conditions  Necessary  for  Ignition.  Pure  barium  sulfate  is 
not  decomposed  appreciably  by  heating  in  dry  air  up  to  a  tempera- 
ture of  1400°.  If  heated  in  the  presence  of  carbon,  carbon  mon- 
oxide, or  other  reducing  agents  it  is  partly  reduced  to  the  sulfide 
even  at  a  temperature  of  600° ;  the  presence  of  moisture  also  seems 
to  favor  this  reduction.  If  the  precipitate  is  ignited  with  the  filter 
paper  without  previous  drying  appreciable  amounts  of  barium 
sulfide  may  form,  unless  the  temperature  is  kept  very  low  until  all 
of  the  water  and  volatile  organic  matter  has  been  driven  off.  If 
some  of  the  precipitate  has  been  reduced  it  can  be  changed  back 
into  the  sulfate  by  moistening  with  dilute  sulfuric  acid,  evaporating 
to  dryness  and  igniting. 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Oxidation  of  the  Sulfur.  Weigh  out  0.5  gm.  of  the  sample 
into  a  150  cc.  beaker,  cover  with  a  watch  glass,  add  10  cc.  of  a 
mixture  of  three  volumes  of  concentrated  nitric  and  one  of  con- 
centrated hydrochloric  acid  and  allow  to  stand  for  ten  minutes. 
If  brown  fumes  are  not  evolved  at  the  expiration  of  this  time  warm 
the  beaker  gently  until  the  mixture  begins  to  react;  if  the  action 
becomes  too  violent,  restrain  it  by  placing  the  beaker  in  a  dish  of 
cold  water.  When  brown  fumes  are  no  longer  given  off  and  when 
the  residue  contains  no  particles  of  a  brassy-yellow  color  it  may  be 


168  QUANTITATIVE  CHEMICAL  ANALYSIS 

assumed  that  the  decomposition  of  the  sample  is  complete.  If 
decomposed  too  rapidly,  yellow  or  greenish-yellow  particles,  which 
consist  for  the  most  part  of  free  sulfur,  will  float  in  or  on  the  solu- 
tion; the  oxidation  should  then  be  completed  by  adding  one  or 
two  drops  of  liquid  bromine  (not  bromine  water)  and  allowing  to 
stand  on  the  steam  bath  for  a  few  minutes. 

Displacement  of  Nitric  Acid.  Remove  the  cover  from  the 
beaker,  rinse  off  the  former  with  a  little  water  and  evaporate  the 
solution  to  dryness  on  the  steam  bath,  then  add  10  cc.  of  dilute 
hydrochloric  acid  and  evaporate  to  dryness  as  before.  Moisten 
the  residue  with  1  or  2  cc.  of  dilute  hydrochloric  acid,  add  50  cc. 
of  water  and  digest  until  all  soluble  salts  have  been  brought  into 
solution,  noting  especially  that  the  ferric  sulfate  present  in  the 
residue  often  dissolves  very  slowly. 

Separation  of  Gangue  and  Iron.  Filter  through  a  7  cm. 
filter  into  a  300  cc.  beaker  and  wash  with  at  least  50  cc.  of  cold 
water.  Dilute  the  filtrate  to  150  cc.,  heat  nearly  to  boiling  and 
add  ammonium  hydroxide  until  the  resulting  mixture  smells  of 
ammonia  and  all  of  the  iron  seems  to  be  precipitated.  Keep  the 
mixture  near  the  boiling  point  for  about  five  minutes,  then  allow 
the  solution  to  stand  till  most  of  the  precipitate  has  settled. 
Decant  off  the  clear  portion  of  the  solution  thru  an  11  cm.  filter, 
receiving  the  filtrate  into  a  500  cc.  beaker,  then  transfer  the 
precipitate  to  the  filter  and  wash  with  hot  water  " churning  up" 
the  precipitate  frequently  with  a  stream  from  the  wash  bottle, 
and  using  about  200  cc.  of  wash  water  in  all;  this  forms  filtrate 
No.  1. 

Set  aside  the  beaker  containing  the  filtrate  and  place  the  beaker 
in  which  the  iron  was  precipitated  under  the  funnel.  Transfer  as 
much  of  the  precipitate  as  can  be  readily  picked  up  by  means  of  a 
stirring  rod  to  the  bottom  of  the  empty  beaker,  taking  care  to  avoid 
rupturing  the  filter;  at  least  three-fourths  of  the  precipitate  can 
be  easily  transferred  by  this  means  in  a  few  minutes.  Add  suffi- 
cient warm  dilute  hydrochloric  acid,  drop  by  drop,  to  the  precipitate 


DETERMINATION  OF  SULFUR  IN   IRON   PYRITES       169 

still  remaining  on  the  filter,  to  completely  dissolve  it,  using  not 
more  than  10  cc.  of  the  reagent,  preferably  less.  Wash  the  filter 
with  cold  water  long  enough  to  remove  the  ferric  chloride  and 
make  it  colorless,  finally  warm  the  mixture  in  the  beaker  until  a 
perfectly  clear  yellow  solution  is  obtained.  Dilute  the  solution  to 
150  cc.,  reprecipitate  the  iron  as  before  and  again  filter  and  wash, 
receiving  the  filtrate  (filtrate  No.  2)  in  a  500  cc.  beaker. 

Precipitation  of  Barium  Sulfate.  Add  to  both  filtrates  (No.  1 
and  2)  a  drop  of  methyl  orange  indicator,  then  dilute  hydrochloric 
acid  until  the  solutions  are  slightly  red  and  then  three  drops  of  acid 
in  excess.  Heat  filtrate  No.  1  to  boiling  and  add  with  constant 
stirring  30  cc.  of  barium  chloride  solution,  1  cc.  of  which  is  equiva- 
lent to  0.01  gm.  of  sulfur,  also  heated  nearly  to  boiling.  Heat 
filtrate  No.  2  in  like  manner  and  add  10  cc.  of  barium  chloride 
solution.  Allow  both  precipitates  to  stand  for  at  least  one  hour, 
then  filter  on  separate  filters  and  wash  thoroughly  with  hot  water 
and  dry. 

Igniting  and  Weighing  Precipitate.  Burn  the  filter  contain- 
ing the  precipitate  from  filtrate  No.  2  in  a  porcelain  or  platinum 
crucible;  separate  the  precipitate  obtained  from  filtrate  No.  1  from 
its  filter  and  burn  the  latter,  in  the  same  crucible.  Finally  add  the 
main  precipitate  to  the  crucible  and  ignite  for  at  least  ten  minutes 
over  a  good  flame,  allow  to  cool  and  weigh  accurately.  Calculate 
the  percentage  of  sulfur  present  in  the  original  sample. 

III.   ADDITIONAL  NOTES  ON  THE  DETERMINATION 

This  determination  is  of  much  industrial  importance  and  has 
been  made  the  subject  of  many  investigations.*  Duplicate  deter- 
minations by  the  method  here  outlined  need  not  differ  by  more 
than  0.2  per  cent,  and  give  very  nearly  the  true  percentage  of 

,«5^ 

*  See  Hinze  and  Webber,  Zeit.  fur  analytische  Chemie,  45,  31  (1906); 
Allen  and  Johnston,  Jour,  of  Industrial  and  Eng.  Chem.,  2,  196  (1910);  Allen 
and  Bishop,  Eighth  Int.  Congress  of  Applied  Chemistry,  Vol.  I,  page  33 

(1913). 


170  QUANTITATIVE  CHEMICAL  ANALYSIS 

sulfur  present.  An  entire  determination  can  be  completed  within 
three  hours  in  addition  to  the  time  the  precipitate  is  allowed  to 
stand  before  filtering 

IV.   QUESTIONS  AND  PROBLEMS.     SERIES  9 

1.  A  lump  of  ore  weighs  500  gm.  and  consists  of  20  per  cent  quartz  (sp.  gr. 
2.8)  and  80  per  cent  pyrite  (sp.  gr.  5).     If  the  sample  is  crushed,  mixed  and 
quartered  twice,  what  is  the  maximum  permissible  size  of  particle  for  both 
crushings  in  order  that  the  0.5  gm.  sample  actually  weighed  out  shall  repre- 
sent the  correct  composition  of  the  sample  to  within  0.1  per  cent? 

2.  What  advantages  are  there  in  keeping  the  nitrate  from  the  two  iron 
precipitates  separate  rather  than  uniting  them? 

,  3.  How  would  you  proceed  in  order  to  determine  the  amount  of  barium 
chloride  occluded  by  the  precipitate  of  barium  sulf ate  found? 

4.  If  the  tendency  for  barium  sulfate  to  occlude  the  magnesium  ion  is 
represented  by  one,  what  numbers  would  represent  its  tendency  to  occlude 
the  sodium,  potassium,  ammonium  and  calcium  ions  if  the  data  given  on 
page  134  is  assumed  to  be  correct? 

6.  If  the  ash  of  the  filter  paper  used  weighed  0.0002  gm.,  how  large  a  de- 
parture from  the  correct  percentage  would  result  from  failure  to  correct  for 
it,  assuming  that  0.5  gm.  of  sample  is  used  and  that  it  contained  40  per  cent 
of  sulfur? 


CHAPTER  XXIV 

SEPARATION   OF   CALCIUM   FROM   MAGNESIUM  AND   PARTIAL 
ANALYSIS   OF  LIMESTONE 

I.  FACTS  UPON  WHICH  THE  ANALYSIS  Is  BASED 

Composition  of  Limestone.  This  rock  invariably  contains,  in 
addition  to  calcium  and  magnesium  carbonates,  small  amounts  of 
the  carbonates  and  oxides  of  iron,  manganese  and  alumina,  and 
more  or  less  quartz,  clay  and  other  silicates.  The  minerals  pyrite, 
graphite,  apatite  and  gypsum  are  frequently  associated  with 
limestone. 

Proximate  Method  of  Analysis.  This  analysis  forms  one  of 
the  problems  frequently  presented  to  the  analyst  since  limestone 
is  an  essential  raw  material  in  many  branches  of  chemical  tech- 
nology. The  complete  analysis  takes  much  time  and  labor,  and 
for  many  technical  uses  is  unnecessary;  hence  in  many  factories 
it  is  customary  to  make  a  more  rapid  " proximate  analysis,"  in 
which  certain  groups  of  constituents,  which  are  present  in  small 
amounts  only,  are  separated  and  reported  as  a  whole,  rather  than 
being  resolved  into  their  ultimate  elements. 

If  the  sample  is  treated  with  nitric  or  hydrochloric  acid  the 
quartz,  graphite  and  most  of  the  silicates  remain  undissolved.  If 
the  amount  of  insoluble  matter  left  is  very  small  it  is  frequently 
ignited,  which  effects  combustion  of  the  graphite,  weighed,  and 
reported  as  "gangue"  or  " insoluble  matter."  If  the  amount 
present  is  larger  it  is  usually  considered  necessary  to  treat  the 
sample  as  an  insoluble  silicate  (see  Chapter  XXVII),  or  to  treat 
the  gangue  matter  which  has  been  separated  as  an  insoluble 

silicate. 

171 


172  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  iron,  aluminum  and  phosphoric  acid  are  almost  invariably 
separated  from  the  other  bases  present  by  the  use  of  ammonium 
hydroxide.  The  resulting  precipitate  can  be  resolved  into  its  ulti- 
mate constituents  by  methods  discussed  in  other  chapters  of  this 
book;  they  are  more  frequently  weighed  together  and  reported 
as  mixed  oxides.  The  small  amount  of  manganese  which  is  some- 
times present  can  be  separated  with  approximate  accuracy  from 
the  filtrate  by  the  addition  of  bromine,  which  causes  this  element  to 
separate  as  the  hydrated  dioxide. 

The  loss  which  results  from  ignition  represents  still  a  third 
group  of  constituents  of  which  carbon  dioxide  is  by  far  the  most 
important;  this  determination  is  sometimes  substituted  for  the 
more  accurate  estimation  of  this  constituent. 

After  eliminating  all  of  the  elements  named  only  calcium  and 
magnesium  remain.  As  the  percentages  of  these  elements  often 
have  an  important  practical  significance  they  are  usually  deter- 
mined with  considerable  care  and  accuracy. 

Sources  of  Error  in  the  Determination  of  Gangue.  This  de- 
termination furnishes  an  illustration  of  a  solution  process  depend- 
ent upon  the  chemical  action  of  a  reagent  (see  Chapter  XXVIII). 
Since  certain  silicates  such  as  clay  are  but  slowly  acted  upon  by 
the  acids  used  the  results  obtained  depend  to  some  extent  upon  the 
fineness  of  the  sample,  the  length  of  time  it  is  treated  and  the 
composition  of  the  acid  used;  there  is  no  generally  accepted 
standard  method  of  procedure.  Sufficient  nitric  acid  should  be 
present  to  dissolve  any  pyrite,  and  to  effect  complete  oxidation  of 
the  ion.  After  decomposition  has  been  effected  the  solution  should 
be  evaporated  to  complete  dryness  to  dehydrate  and  render  in- 
soluble the  silicic  acid  formed  (see  Chapter  XXVII). 

Sources  of  Error  in  the  Determination  of  Iron  and  Alumina. 
Ferric  hydroxide  and  aluminum  hydroxide  form  bulky  precipitates, 
which  are  extremely  difficult  to  filter  and  wash.  When  separated 
by  the  addition  of  ammonium  hydroxide,  from  a  solution  which 
also  contains  calcium  and  magnesium,  the  resulting  precipitate 


SEPARATION   OF   CALCIUM   FROM   MAGNESIUM          173 

invariably  contains  these  elements  also,  even  tho  a  large  amount 
of  ammonium  chloride  was  present.  This  is  due  in  part  to  the 
difficulty  of  washing  the  precipitate  and  to  occlusion;  it  may  also 
have  resulted  from  the  absorption  of  carbon  dioxide  by  the  reagent 
before  use  or  by  the  mixture  after  precipitation  and  formation  of 
insoluble  calcium  carbonate. 

Ammonium  hydroxide  acts  upon  glass,  especially  the  ordinary 
soft  glass,  appreciably,  and  solutions  which  have  stood  in  bottles 
for  some  time  invariably  contain  a  scale-like  precipitate  which  is 
largely  composed  of  silica;  it  can  be  removed  by  filtration,  but  the 
filtered  solution  may  still  contain  small  amounts  of  soluble  silica, 
some  of  which  may  separate  when  the  reagent  is  used.  Hence 
when  results  of  the  greatest  accuracy  are  demanded  this  precipita- 
tion must  be  made  in  vessels  of  resistant  glass  or  still  better  of 
platinum,  and  the  ammonium  hydroxide  used  must  be  freshly 
distilled.  In  commercial  work  the  only  precaution  usually  taken 
is  to  filter  the  reagent,  and  to  reduce  its  concentration  and  the  time 
it  is  in  contact  with  the  containing  vessel  to  a  minimum. 

The  hydroxides  of  iron  and  aluminum  are  converted  into  the 
corresponding  oxides  at  a  temperature  of  about  600°  and  much 
higher  temperatures  can  be  used  without  danger  of  further  changes. 
Ferric  oxide  is  easily  reduced  to  lower  oxides  by  organic  matter  at 
this  temperature. 

Properties  of  Calcium  and  Magnesium  Oxalates.  Crystalline 
calcium  oxalate  (CaC204  •  2  H20)  dissolves  in  water  to  the  extent 
of  5.6  mg.  per  liter.  If  precipitated  from  an  alkaline  solution  it  is 
finely  divided  and  bulky,  but  if  precipitated  from  an  acid  solution 
it  is  coarsely  crystalline.  It  occludes  magnesium,  and  to  a  less 
extent  sodium,  potassium  and  ammonium  salts,  probably  as  the 
result  of  its  tendency  to  form  double  salts  of  these  metals.  The 
amount  of  occlusion  is  reduced  by  precipitating  from  a  solution 
containing  a  slight  excess  of  free  acid;  under  such  conditions, 
however,  the  precipitation  is  incomplete  and  altho  about  80  per 
cent  can  be  separated  from  a  solution  which  is  distinctly  acid,  the 


174  QUANTITATIVE  CHEMICAL  ANALYSIS 

remainder  must  be  separated  from  a  solution  which  is  distinctly 
alkaline.  For  these  reasons  it  is  decidedly  preferable  to  separate 
most  of  the  precipitate  by  the  addition  of  a  solution  of  oxalic  acid 
to  the  neutral  or  barely  acid  calcium-containing  solution,  and  the 
balance  by  neutralizing  the  resulting  mixture.  A  reagent  which 
contains  45  gm.  of  crystallized  oxalic  acid  (C2H204  •  2  H20)  per  liter  / 
(1  cc.  of  which  is  equivalent  to  0.02  gm.  of  CaO)  is  a  convenient 
one  to  employ. 

Magnesium  oxalate  (MgC204  •  2  H20)  is  soluble  in  water  to  the 
extent  of  300  mg.  per  liter,  but  shows  a  remarkable  tendency  to 
form  supersaturated  solutions,  so  that  the  apparent  solubility  may 
rise  to  three  hundred  times  the  normal  value.  Supersaturated 
solutions  of  this  kind  deposit  a  large  part  of  the  excess  of  dissolved 
salt  rapidly  but  much  of  it  is  retained  in  solution  even  after  long 
standing. 

Calcium  is  not  completely  precipitated  from  solutions  containing 
large  amounts  of  magnesium  salts  unless  an  excess  of  C2C>4  ions 
are  present.  If  sufficient  C204  ions  are  present  to  combine  with 
both  the  calcium  and  magnesium  present  the  precipitation  is 
complete;  excessive  concentrations  of  C2C>4  ions  must  be  avoided 
to  prevent  the  solution  from  becoming  supersaturated  with  respect 
to  magnesium  oxalate. 

The  properties  of  these  oxalates  which  are  enumerated  above 
make  it  necessary  to  adopt  and  adhere  to  certain  definite  conditions 
in  separating  calcium  from  magnesium.  The  weight  of  oxalic  acid 
used,  as  compared  with  the  weights  of  calcium  and  magnesium 
present,  and  the  total  volume  from  which  the  precipitate  is  made 
to  separate  are  of  especial  importance.  The  directions  which  are 
given  below  are  especially  designed  for  the  analysis  of  limestone;* 
they  also  apply  to  samples  in  which  the  proportion  of  magnesium 
to  calcium  is  much  greater  than  thab  found  in  limestone  provided 
the  amount  used  is  sufficient  to  furnish  a  total  weight  of  0.4  gm. 
of  the  two  oxides. 

*  Jour,  of  Amer.  Chem.  Soc.,  31,  918  (1909). 


SEPARATION  OF  CALCIUM  FROM  MAGNESIUM          175 

Theory  of  the  Method  Used.  The  occlusion  of  magnesium  by 
calcium  oxalate  has  been  made  the  subject  of  many  investigations, 
but  it  was  first  shown  by  Richards  *  that  the  error  from  this  source 
could  be  greatly  reduced  by  the  presence  of  large  concentrations 
of  NH4  ions  or  of  small  concentrations  of  hydrogen  ions.  This 
seems  to  be  due  to  the  fact  that  a  large  concentration  of  NH4  ions 
must  increase  that  of  the  complex  magnesium-ammonium  ion 
and  reduce  that  of  the  simple  magnesium  ion,  and,  therefore,  that 
of  the  undissociated  magnesium  oxalate.  Similarly,  since  the 
hydrogen  ion  represses  the  ionization  of  oxalic  acid,  it  reduces  the 
concentration  of  the  C204  ion,  and,  therefore,  that  of  the  undisso- 
ciated magnesium  oxalate.  As  the  amount  of  occlusion  depends 
upon  the  concentration  of  the  undissociated  magnesium  oxalate 
either  reagent  should  reduce  the  error  from  this  source. 

Weighing  the  Calcium  Precipitate.  Although  crystallized  cal- 
cium oxalate  loses  most  of  its  water  at  200°  it  is  difficult  to  expel 
all  of  it  without  causing  some  of  the  precipitate  to  decompose  into 
calcium  carbonate  and  carbon  monoxide.  It  can  be  completely 
changed  into  the  carbonate  by  heating  for  a  long  time  at  400°  or 
into  the  oxide  by  heating  to  850°.  As  the  oxide  rapidly  absorbs 
both  water  and  carbon  (S.xide  it  must  be  weighed  in  a  covered 
crucible  as  rapidly  as  possible. 

The  Separation  of  Magnesium.  The  filtrate  from  the  calcium 
has  a  large  volume  and  contains  a  large  amount  of  ammonium 
chloride  and  some  ammonium  oxalate.  These  conditions  make  it 
necessary  to  modify  somewhat  the  method  used  in  Chapter  XXI. 
The  large  concentration  of  the  NH4  ion  greatly  retards  the  sepa- 
ration of  the  precipitate  and  gives  it  an  abnormal  composition. 
Hence  it  becomes  necessary  to  concentrate  the  solution,  to  make 
a  preliminary  precipitation  in  which  the  precipitate  is  allowed  to 
stand  for  ten  hours,  to  separate  and  redissolve  this  precipitate  and 
to  make  a  final  precipitation  as  in  the  analysis  of  magnesium 
sulfate. 

*  Proc.  Am.  Acad.  of  Arts  and  Sciences,  36,  375  (1901). 


176  QUANTITATIVE   CHEMICAL  ANALYSIS 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Separation  of  the  Gangue.  Weigh  out  about  .7  gm.  of  the. 
finely-ground  sample  into  a  200  cc.  beaker,  cover  with  a  watch 
glass  and  gradually  introduce  20  cc.  of  dilute  hydrochloric  and  5 
of  dilute  nitric  acid.  When  violent  action  ceases,  heat  the  beaker 
on  a  steam  bath  long  enough  to  insure  complete  decomposition, 
that  is,  until  no  more  gases  are  liberated.  Then  remove  the 
watch  glass,  rinsing  off  the  under  surface  with  a  stream  from 
a  wash  bottle,  and  evaporate  to  complete  dryness.  To  the  residue 
add  10  cc.  of  dilute  hydrochloric  acid  and  digest  five  minutes,  or 
until  the  basic  salts  or  oxides  which  may  have  formed  have  been 
entirely  dissolved.  Add  20  cc.  of  water,  filter  thru  a  7  cc.  filter, 
wash  four  times  with  10  cc.  portions  of  water  and  drain.  Place  the 
still  moist  filter  in  a  weighed  crucible  and  heat  cautiously  over  a 
wire  gauze  until  the  water  has  been  expelled  and  the  paper  con- 
sumed; finally  ignite  over  a  direct  flame  for  about  ten  minutes, 
then  cool  and  weigh  accurately.  Calculate  and  report  the  per 
cent  of  gangue  present. 

Separation  of  Iron  and  Aluminum.  Warm  the  filtrate  from 
the  gangue  and  add  to  it  slowly  and  with  constant  stirring  recently 
filtered  ammonium  hydroxide  until  the  solution  smells  distinctly 
of  the  reagent.  Place  the  beaker  on  the  sand  bath  and  keep  at  a 
temperature  slightly  below  the  boiling  point  for  about  ten  minutes, 
or  until  the  odor  while  still  easily  recognizable  is  not  unpleasantly 
strong.  This  should  cause  the  separation  of  a  small  amount  of  a 
precipitate  whose  color  may  vary  from  red-brown  to  white.  Filter 
on  a  7  or  9  cm.  filter  and  wash  with  hot  water  until  free  from 
chlorine.  If  the  amount  of  precipitate  is  small,  treat  it  like  the 
gangue  and  report  the  total  percentage.  If  it  is  large,  it  should 
be  redissolved  and  reprecipitated  as  in  the  analysis  of  pyrite, 
except  that  the  two  filtrates  should  be  combined. 

Determination  of  Manganese.  Add  20  cc.  of  bromine  water, 
cover  with  a  watch  glass  and  set  aside  for  twelve  hours. 


SEPARATION  OF  CALCIUM   FROM   MAGNESIUM          177 

Filter  off  the  brown  precipitate  which  should  separate  if  man- 
ganese is  present,  wash,  ignite  and  weigh  as  in  the  determination 
of  gangue.  Calculate  and  report  the  percentage  of  MnO  corre- 
sponding to  the  weight  of  Mn304  thus  found. 

Determination  of  Calcium.  Boil  the  filtrate  until  the  bromine 
is  expelled,  dilute  to  300  cc.,  add  a  drop  of  methyl  orange  indicator 
and  then  hydrochloric  acid  until  the  solution  changes  color  from 
yellow  to  pink.  Heat  to  boiling  and  add  slowly  and  with  con- 
stant stirring  22  cc.  of  oxalic  acid  solution,  set  aside  for  ten. 
minutes,  then  add  very  slowly,  that  is,  over  an  interval  of  at 
least  five  minutes,  3  cc.  of  ammonium  hydroxide,  which  has  been 
diluted  to  30  cc.  with  water.  If  this  does  not  make  the  solu- 
tion distinctly  alkaline  add  a  further  quantity  of  the  reagent  in 
the  same  manner.  After  the  precipitate  has  stood  for  an  hour, 
filter  thru  a  9  cm.  filter  and  wash  with  water  until  free  from 
chlorine.  Place  the  filter  in  a  porcelain  or  platinum  crucible, 
which  has  been  weighed  with  its  cover,  and  destroy  the  filter  as 
in  the  determination  of  gangue;  finally  heat  the  crucible  over  a 
Meker  or  Chaddock  burner  for  at  least  twenty  minutes.  Cool 
in  a  desiccator  for  thirty  minutes,  and  weigh  as  rapidly  as 
possible.  Continue  igniting  and  weighing  until  two  consecutive 
weighings  do  not  differ  by  more  than  0.3  mg.  Calculate  and 
report  the  percentage  of  calcium  oxide  thus  obtained. 

Determination  of  Magnesium.  Acidify  the  filtrate  from  the 
calcium  with  dilute  hydrochloric  acid,  evaporate  to  a  volume  of 
200  cc.  and  cool.  Add  25  cc.  of  the  sodium  phosphate  reagent, 
then  slowly  introduce  25  cc.  of  dilute  ammonium  hydroxide,  which 
should  impart  a  strong  odor  of  ammonia  to  the  solution,  and 
finally  set  aside  for  at  least  ten  hours.  Decant  off  the  clear  solu- 
tion thru  a  9  cm.  filter,  place  a  clean  100  cc.  beaker  under  the  filter 
and  pour  thru  it  the  smallest  possible  amount  of  hydrochloric  acid 
needed  to  dissolve  the  precipitate  on  the  filter  and  in  the  beaker, 
some  5.  cc.  of  the  reagent  diluted  to  25  cc.  should  suffice;  ,hen 
wash  the  filter  free  of  soluble  compounds. 


178  QUANTITATIVE  CHEMICAL  ANALYSIS 

Next  add  to  the  solution  in  the  beaker,  which 'should  have  a 
volume  of  about  50  cc.,  5  cc.  of  sodium  phosphate  solution  and  then 
sufficient  ammonium  hydroxide  to  make  it  distinctly  alkaline  and 
give  an  excess  of  3  cc.  Stir  the  mixture  occasionally  during  an 
interval  of  twenty  minutes,  then  filter  on  a  9  cm.  filter  and  wash 
with  dilute  ammonium  hydroxide  as  in  the  analysis  of  magnesium 
sulfate. 

Separate  the  precipitate  and  weigh  as  in  the  analysis  of  magne- 
sium sulfate.  Calculate  the  percentage  of  magnesium  oxide 
present. 

Determination  of  Hygroscopic  Water.  Weigh  out  0.8  gm.  of 
the  sample  in  a  10  cc.  platinum  or  porcelain  crucible,  which  is 
provided  with  a  cover.  Place  in  a  drying  oven  and  heat  to  a 
temperature  of  105°  for  an  hour,  and  weigh  accurately.  Calculate 
the  per  cent  of  hygroscopic  water  from  the  loss  in  weight  thus 
found. 

Determination  of  Loss  on  Ignition.  Place  the  crucible  con- 
taining the  residue  from  the  previous  determination  on  a  wire 
triangle  and  heat  over  a  Meker  or  Chaddock  burner  until  the 
weight  is  constant,  using  all  of  the  precautions  used  in  the  ignition 
of  the  calcium  oxalate  precipitate.  Calculate  the  percentage  loss 
and  report  as  loss  on  ignition. 

Finally  recalculate  all  the  percentages  thus  far  obtained  to  show 
the  composition  of  the  water-free  sample. 


III.    QUESTIONS  AND  PROBLEMS.    SERIES  10 

1.  If  the  sample  of  limestone  used  for  this  analysis  contained  small  amounts 
of  strontium  or  barium  carbonates^  in  what  manner  would  it  have  affected 
the  determinations  here  outlined? 

»   2.   Under  what  conditions  would  it  be  possible  to  dehydrate  calcium  oxalate 
without  changing  some  of  it  into  the  carbonate? 

3.  How  can  you  determine  from  the  curves  of  Fig.  16  whether  heat  is 
absorbed  or  liberated,  when  you  determine  the  loss  or  ignition? 


SEPARATION  OF  CALCIUM  FROM  MAGNESIUM          179 

5.  A  sample  of  limestone  consists  of  90  per  cent  CaCO3,  3  per  cent  MgCOs, 
3  per  cent  CaSO4  •  2  H2O  and  3  per  cent  SiO2,  what  numerical  difference  would 
you  expect  between  the  true  per  cent  of  CO2  and  the  loss  on  ignition? 

f  6.  Suppose  that  in  the  analysis  of  the  limestone  described  above  there  was 
a  positive  error  of  5  mg.  in  the  calcium  precipitate  owing  to  occlusion  of  mag- 
nesium, what  percentage  error  would  appear  in  the  determination  of  the  mag- 
nesium? 

/  7.  Suppose  a  sample  of  limestone  contained,  in  addition  to  5  per  cent  of 
insoluble  silicates,  only  CaCO3  and  MgCOs,  and  suppose  further  that  the  loss 
on  ignition  amounted  to  45  per  cent,  what  could  you  infer  regarding  the  per- 
centages of  calcium  and  magnesium? 


CHAPTER  XXV 

ANALYSIS   OF  ALLOYS   CONTAINING   TIN  AND   LEAD 
I.   FACTS  UPON  WHICH  THE  METHOD  Is  BASED 

Composition  of  Samples.  These  alloys  contain  from  20  to 
70  per  cent  of  tin  and  are  used  as  solders;  their  market  value 
depends  mainly  upon  the  percentage  of  tin  present  which  is  the 
more  expensive  metal.  Traces  of  other  metals,  especially  copper, 
zinc,  iron  and  antimony  are  sometimes  present.  As  the  alloy  is 
usually  cast  and  sold  in  the  form  of  long,  thin  bars,  which  are 
fairly  homogeneous,  an  average  sample  is  easily  obtained  by  cutting 
thin  shavings  from  the  length  of  the  bar. 

Decomposition  of  the  Alloy.  Alloys  which  contain  large  per- 
centages of  lead  are  but  slowly  attacked  by  either  sulfuric  or  hydro- 
chloric acids,  largely  owing  to  the  slight  solubility  of  the  sulfate 
and  chloride  of  lead;  dilute  nitric  acid  acts  more  energetically,  and 
forms  lead  nitrate  and  metastannic  acid;  concentrated  nitric  acid 
acts  more  slowly,  owing  to  the  slight  solubility  of  lead  nitrate  in 
strong  nitric  acid.  If  dissolved  in  concentrated  nitric  acid,  or  if 
dissolved  in  dilute  nitric  and  evaporated  to  dryness  the  tin  present 
is  completely  changed  into  metastannic  acid.  This  treatment  also 
favors  the  separation  of  metastannic  acid  in  a  form  which  permits 
of  easy  and  rapid  filtration. 

Properties  of  Metastannic  Acid.  The  solubility  of  this  com- 
pound in  water  and  dilute  nitric  acid  is  not  known,  it  is  probably 
very  small;  its  solubility  in  dilute  hydrochloric  is  greater,  and  in 
dilute  sulfuric  it  is  quite  large.  It  possesses  a  remarkable  tendency 
to  occlude  metals,  especially  iron,  lead,  copper,  zinc  and  man- 
ganese, probably  owing  to  the  formation  of  insoluble  salts  of 

180 


ANALYSIS  OF   ALLOYS  CONTAINING  TIN  AND  LEAD      181 

metastannic  acid.     The  amount  of  lead  occluded  when  tin-lead 
alloys  are  decomposed  is  less  when  the  nitric  acid  used  is  very 
strong,  but  even  under  the  most  favorable  circumstances  the  error ' 
from  this  source  is  too  large  to  neglect  when  the  precipitate  amounts 
to  more  than  a  few  milligrams. 

Freshly  precipitated  metastannic  acid  is  readily  dissolved  by 
moderately  strong  solutions  of  ammonium  sulfide  with  the  forma- 
tion of  ammonium  sulf ostannate ;  if  precipitates  which  contain 
any  of  the  occluded  metals  named  above  are  treated  with  this 
reagent  these  metals  separate  as  insoluble  sulfides.  If  nitric  acid 
is  added  to  a  solution  of  ammonium  sulfostannate,  a  mixture  of 
sulfur  and  stannic  sulfide  separates,  but  when  the  concentration 
of  the  acid  is  large,  or  if  the  mixture  is  heated,  the  stannic  sulfide 
slowly  forms  metastannic  acid.  The  resulting  mixture  is  difficult 
to  filter,  owing  to  the  fineness  of  the  particles.  If  a  solution  of 
ammonium  sulf  ostannate  is  evaporated  to  complete  dryness  and 
the  residue  treated,  first  with  dilute  and  then  with  concentrated 
nitric  acid,  the  sulfur  which  separates  can  be  fused  into  a  single 
globule,  which  can  be  readily  removed;  the  metastannic  acid  can 
then  be  separated  by  filtration  and  ignited  without  being  recon- 
verted into  stannic  sulfide. 

Metstannic  acid  is  slowly  but  completely  converted  into  stannic 
oxide  by  heating  to  500°.  It  is  easily  reduced  by  organic  matter 
even  at  lower  temperatures;  the  oxide  is  not  appreciably  hygro- 
scopic. 

Properties  of  Lead  Sulfate.  This  is  a  pulverulent  precipi- 
tate; it  has  a  specific  gravity  of  6.23,  settles  rapidly  and  as  much 
as  1  gm.  of  it  can  be  readily  filtered  and  washed.  Its  solubility 
in  pure  water  is  about  44  mg.  per  liter.  This  is  reduced  by  the 
addition  of  sulfuric  acid  up  to  the  point  at  which  the  mixture 
contains  about  10  per  cent  by  volume  of  the  concentrated  acid; 
beyond  this  concentration  the  solubility  begins  to  increase.  It 
is  also  increased  by  the  presence  of  even  small  concentrations  of 
hydrochloric  and  nitric  acids,  and  in  the  quantitative  separation 


182  QUANTITATIVE  CHEMICAL  ANALYSIS 

of  lead  sulfate  these  acids  must  be  expelled  by  evaporating  with 
an  excess  of  sulfuric  acid.  Its  solubility  is  greatly  decreased  by 
the  presence  of  even  small  concentrations  of  alcohol. 

Pure  lead  sulfate  can  be  heated  without  danger  of  decomposition 
up  to  400°.  As  it  is  very  easily  reduced  by  heating  in  the  presence 
of  organic  matter,  and  as  the  metal  is  decidedly  volatile,  extreme 
care  must  be  taken  in  igniting  the  precipitate. 

II.   OUTLINE  OF  THE  METHOD  OF  ANALYSIS 

Preparation  and  Decomposition  of  the  Sample.  Prepare  the 
sample  by  cutting  about  2  gm.  of  thin  shavings  from  a  bar  of  the 
alloy  by  means  of  a  dull  knife,  and  place  in  a  clean,  dry  sample  tube. 
Weigh  out  0.5  gm.  of  the  sample  into  a  200  cc.  beaker,  cover  with 
a  watch  glass,  add  10  cc.  of  concentrated  nitric  acid  and  then  from 
5  to  10  cc.  of  water,  using  the  larger  amount  if  the  sample  is  but 
slowly  attacked.  Heat  the  beaker  on  the  steam  bath  long  enough 
to  disintegrate  the  sample,  that  is,  until  all  hard  lumps  have  disap- 
peared and  a  fine  white  powder  only  remains;  then  remove  the 
cover  and  evaporate  to  dry  ness. 

Separation  and  Purification  of  Metastannic  Acid.  Add  to  the 
residue  5  cc.  of  concentrated  nitric  acid  and  30  cc.  of  water, 
heat  nearly  to  boiling  and  digest  for  ten  minutes;  while 
waiting  prepare  a  glass  filter  tube  with  a  thin  layer  of  finely 
shredded  asbestos  and  connect  with  a  clean  filter  flask.  Pass  the 
liquid  in  the  beaker  thru  the  filter,  refiltering  if  necessary,  to  obtain 
a  perfectly  clear  filter,  and  wash  three  times  with  10  cc.  portions 
of  water.  Transfer  the  filtrate  to  a  clean  250  cc.  beaker,  wash  out 
the  flask  with  at  least  four  portions  of  water  and  place  on  a  steam 
or  sand  bath  to  evaporate. 

Invert  the  filter  tube  over  the  bottom  of  a  clean  200  cc.  beaker, 
push  the  filter  plate  and  asbestos  into  the  beaker  by  means  of  a 
glass  rod  or  wire  passed  thru  the  stem  of  the  tube,  and  rinse  any 
adhering  fibers  of  asbestos  into  the  beaker  by  a  few  cubic  centi- 
meters of  water.  Next  remove  the  filter  plate  and  rinse  this  also, 


ANALYSIS  OF  ALLOYS  CONTAINING  TIN  AND  LEAD      183 

then  add  10  cc.  of  colorless  or  nearly  colorless  ammonium  sulfide. 
Disintegrate  the  asbestos  by  means  of  a  glass  rod,  warm  the  mix- 
ture slightly  until  all  white  particles  have  been  dissolved  and  only 
a  fine  black  residue  of  lead  sulfide  remains.  Prepare  a  second 
asbestos  filter,  moisten  with  a  few  drops  of  ammonium  sulfide 
solution,  filter  the  solution  of  sulfostannate  of  tin  thru  it,  wash  four 
times  with  water  containing  a  few  drops  of  ammonium  sulfide  and 
twice  with  pure  water.  Transfer  the  solution  in  the  filter  flask  to  a 
clean  400  cc.  beaker,  wash  four  times  with  water,  place  on  a. steam 
or  sand  bath  and  evaporate  to  complete  dryness.  Warm  about  5 
cc.  of  dilute  hydrochloric  acid  in  a  small  beaker  and  pour  over  the 
filter  containing  the  lead  precipitate,  which  should  cause  the  filter 
to  become  pure  white,  then  wash  with  hot  water  and  transfer  the 
solution  to  the  beaker  containing  the  main  part  of  the  lead. 

Determination  of  Lead.  Add  to  the  beaker  containing  the 
lead  solution  5  cc.  of  concentrated  sulfuric  acid,  which  should 
be  introduced  cautiously  if  the  solution  is  hot;  evaporate  on 
the  sand  bath  till  white  fumes  of  sulfur  trioxide  are  given  off, 
watching  the  mixture  very  carefully  during  the  later  stages  of  the 
process  as  it  may  bump  and  sputter.  When  cool,  add  45  cc.  of 
water  and  set  aside  for  at  least  one-half  hour.  While  waiting 
for  the  completion  of  these  operations,  prepare  a  Gooch  crucible 
with  a  good  layer  of  asbestos;  ignite  and  weigh  accurately.  Fil- 
ter the  lead  sulfate  precipitate  thru  the  crucible  thus  prepared, 
wash  four  times  with  10  cc.  portions  of  20  per  cent  alcohol,  dry 
at  about  200°  and  weigh.  Calculate  the  percentage  of  lead  present. 

Determination  of  Tin.  Add  to  the  beaker  containing  the 
dry  residue  resulting  from  the  evaporation  of  the  sulfostannate 
solution  10  cc.  of  dilute  nitric  acid,  cover  at  once  with  a  watch 
glass  and  warm  gently  till  further  action  ceases,  next  add  10  cc. 
of  concentrated  nitric  acid  and  again  warm  for  a  few  minutes. 
Rinse  off  the  sides  of  the  beaker  and  the  watch-glass  cover  and 
set  the  latter  aside,  then  evaporate  the  mixture  to  nearly  complete 
dryness.  The  large  amount  of  sulfur  which  separates  in  a  free 


184  QUANTITATIVE  CHEMICAL  ANALYSIS 

condition  should  finally  fuse  to  form  a  clear  yellow  liquid,  all  of 
which  should  be  collected  into  a  single  large  globule  before  it 
solidifies. 

Add  to  the  residue  5  cc.  of  dilute  nitric  acid  and  50  cc.  of 
water,  digest  for  ten  minutes,  then  filter  on  a  9  cm.  filter  and 
9  wash  free  from  acid  for  if  much  acid  is  left  in  contact  with  the  pre- 
cipitate the  filter  will  become  brittle  and  will  crumble  on  drying. 
Separate  the  filter  as  completely  as  possible  from  the  precipitate 
and  set  the  latter  aside  on  a  watch  glass.  Remove  the  globule 
of  sulfur  from  the  precipitate,  which  may  contain  very  small 
amounts  of  tin,  and  burn  in  the  crucible.  Next,  burn  the  filter 
in  the  crucible  and  finally  add  the  main  precipitate  and  ignite  over 
a  wire  triangle  with  a  Meker  burner  or  blast  lamp,  for  twenty 
minutes.  If  the  resulting  precipitate  is  decidedly  gray  moisten 
with  a  few  drops  of  concentrated  nitric  acid,  evaporate  off  the  acid, 
and  again  ignite.  Calculate  the  percentage  of  tin  from  the  weight 
of  stannic  oxide  found. 

III.  QUESTIONS  AND  PROBLEMS.     SERIES  11 

1.  Show  how  the  action  of  nitric  acid  on  metallic  tin  might  give  rise  to  either 
stannous  nitrate,  stannic  nitrate  or  metastannic  acid. 

2.  Indicate  the  reaction  of  ammonium  sulfide  on  the  tin-lead  precipitate. 

3.  What  determines  the  volume  of  sulfuric  acid  which  should  be  added  to 
the  solution  which  contains  the  lead  before  evaporating  to  dryness? 

4.  What  factors  make  it  easy  to  completely  displace  the  nitric  acid  from 
this  solution? 

6.   What  effect  would  you  expect  the  presence  of  large  amounts  of  Cu, 
Fe,  Zn  and  Sb  to  have  on  the  method? 


vJV,rs 


>•»  +- 

f  f 


CHAPTER  XXVI 

ANALYSIS   OF  BRASS 
I.   FACTS  UPON  WHICH  THE  METHOD  Is  BASED 

Composition  of  Sample.  The  essential  constituents  of  this 
alloy  are  copper  and  zinc;  it  sometimes  contains  small  percentages 
of  tin  and  lead  and  traces  of  iron,  antimony  and  other  metals, 
which  represent  impurities  in  the  metals  of  which  the  alloy  was 
made.  A  homogeneous  sample  can  usually  be  obtained  by  drilling 
holes  in  the  ingot  or  bar,  or  by  placing  in  a  turning  lathe  and  cutting 
thin  shavings  from  it.  If  the  sample  has  been  already  made  into 
drillings  or  shavings  it  should  be  carefully  examined  for  particles 
of  wood  or  iron  with  which  it  is  sometimes  contaminated. 

Conditions  for  Separation  of  Tin  and  Lead.  The  alloy  is 
readily  dissolved  in  either  strong  or  dilute  nitric  acid  and  essentially 
the  same  conditions  as  were  used  for  the  determination  of  tin  and 
lead  in  solder  can  be  used  here.  The  amount  of  tin  present  is 
usually  so  small  that  it  is  not  ordinarily  necessary  to  purify  it  for 
occluded  metals. 

Conditions  for  Separation  of  Copper  from  Zinc.  The  decom- 
position voltage  of  copper  is  0.33  volt  lower  and  that  of  zinc  0.71 
volt  higher  than  that  of  hydrogen,  hence  the  two  metals  are 
easily  separated  in  the  presence  of  sufficient  free  acid  by  the 
constant  current  method.  But  little  difficulty  is  experienced  in 
obtaining  good  deposits  of  copper  in  the  presence  of  N03  ions, 
and  currents  of  0.5  ampere  normal  density  can  be  used  if  a  gauze 
electrode  is  employed.  If  a  foil  electrode  is  used  it  is  scarcely  safe 
to  use  currents  greater  than  0.05  ampere  normal  density.  The 
precipitated  metal  is  rapidly  dissolved  by  even  dilute  nitric  acid 
and  is  slowly  oxidized  even  at  a  temperature  of  100°. 

185 


186  QUANTITATIVE  CHEMICAL  ANALYSIS 

Conditions  for  Determination  of  Zinc  as  Phosphate.  When  a 
soluble  phosphate  is  added  to  a  neutral  solution  of  a  zinc  salt  which 
also  contains  a  large  concentration  of  ammonium  salts,  a  flocculent 
precipitate  separates;  if  this  precipitate  is  digested  for  a  short 
time  it  is  slowly  converted  into  a  crystalline  precipitate  having 
the  formula  Zn(NH4)P04  •  H20.  This  precipitate  is  appreciably 
soluble  in  solutions  containing  even  small  concentrations  of  either 
hydrogen  or  hydroxyl  ions;  hence  the  solution  must  be  made  as 
nearly  neutral  as  possible.  It  is  also  essential  that  the  solution 
should  contain  a  large  concentration  of  NH4  ions  and  a  large  ex- 
cess of  P04  ions.  The  solubility  of  the  precipitate  in  either  hot 
or  cold  water  is  but  slight,  and  it  is  easily  washed  free  from  soluble 
salts. 

The  crystalline  zinc  ammonium  phosphate  readily  loses  all  of 
its  water  if  dried  at  105°;  it  can  also  be  converted  into  the  pyro- 
phosphate  on  direct  ignition,  but,  as  with  the  corresponding  trans- 
formation of  the  magnesium  compound,  it  readily  undergoes 
partial  reduction  and  fuses  at  a  bright  red  heat;  hence  it  is  pref- 
erable to  separate  on  a  Gooch  crucible  rather  than  on  a  paper 
filter. 

II.  OUTLINE  OF  THE  METHOD  OF  PROCEDURE 

Determination  of  Tin.  Weigh  out  3  gm.  of  the  sample  into 
a  100  cc.  beaker,  add  25  cc.  of  dilute  nitric  acid  and  cover  with 
a  watch  glass.  Action  should  begin  to  take  place  almost  at  once 
and  complete  solution  should  be  effected  within  a  few  minutes;  if 
not,  warm  the  beaker  slightly  by  placing  on  the  steam  bath.  If 
the  action  at  any  time  becomes  too  violent  it  should  be  restrained 
by  placing  the  beaker  in  a  vessel  of  cold  water.  When  the  alioy 
is  completely  dissolved  remove  and  rinse  off  the  watch-glass  cover, 
again  place  on  the  steam  bath,  and  allow  to  evaporate  to  complete 
dryness. 

Add  to  the  residue  5  cc.  of  dilute  nitric  acid  and  25  cc.  of  water 
and  allow  to  digest  till  the  basic  salts  of  copper,  which  usually 


ANALYSIS  OF  BRASS  187 

separate  as  a  voluminous  blue-white  precipitate,  are  brought  into 
solution.  If  a  fine  white  residue  of  metastannic  acid  still  remains, 
filter  on  a  small  filter,  wash  till  free  from  acid,  dry,  ignite  and  weigh. 
Calculate  the  percentage  of  tin  from  the  stannic  oxide  thus  found. 

Determination  of  Lead.  Add  to  the  filtrate  from  the  tin  7  cc. 
of  concentrated  sulfuric  acid  and  evaporate  until  the  nitric  acid 
has  been  expelled  and  dense  white  fumes  of  sulfur  trioxide  are 
given  off.  This  will  not  occur  until  the  total  volume  is  less  than 
7  cc.  and  the  temperature  of  the  solution  has  risen  to  about  250°. 
During  the  evaporation  of  the  solution  the  sulfates  of  lead,  copper 
and  zinc  separate,  and  unless  the  precipitate  is  kept  in  constant 
motion,  and  unless  the  temperature  is  kept  below  100°,  violent 
bumping  and  spiriting  is  certain  to  take  place.  For  this  reason 
it  is  best  to  evaporate  on  the  steam  bath  until  most  of  the  water 
is  driven  off,  and  to  complete  the  evaporation  on  a  sand  bath  or 
sheet  of  asbestos  while  stirring  the  mixture  vigorously  and  con- 
tinuously. 

When  the  dish  is  cold  add  50  cc.  of  water,  stir  until  the 
soluble  sulfates  have  been  dissolved  and  only  sulfate  of  lead 
remains,  then  set  aside  for  half  an  hour.  While  waiting  for  these 
operations,  prepare  and  weigh  accurately  a  Gooch  crucible,  con- 
nect the  crucible  with  a  clean  filter  flask,  filter  off  the  precipi- 
tate on  it,  wash  four  times  with  a  mixture  of  equal  parts  of  water 
and  dilute  sulfuric  acid,  and  twice  with  20  per  cent  alcohol.  Heat 
the  crucible  slowly  to  a  temperature  of  about  250°,  cool  and 
weigh  accurately.  Calculate  the  percentage  of  lead  present  from 
the  weight  of  lead  sulfate  thus  found. 

Division  of  the  Solution.  Transfer  the  solution  containing 
the  copper  and  zinc  to  a  250  cc.  graduated  flask,  dilute  till  the 
lowest  part  of  the  meniscus  corresponds  to  the  line  on  the  neck  of 
the  flask,  stopper  with  a  tightly  fitting  cork  and  mix  thoroughly 
by  alternately  inverting  and  rotating  the  flask.  Measure  out 
three  50  cc.  portions  of  the  solution  as  follows:  pour  out  about 
20  cc.  of  the  brass  solution  in  a  small  beaker  and  use  this  to  rinse 


188  QUANTITATIVE   CHEMICAL   ANALYSIS 

out  a  clean  but  not  necessarily  dry  50  cc.  pipet,  discarding  the 
solution  after  using  it.  Next,  suck  up  a  further  quantity  of  the 
liquid  into  the  pipet  until  it  rises  above  the  mark  on  the  stem  of 
the  pipet  and  allow  to  drain  back  into  the  flask  until  the  lowest  point 
on  the  curve  of  the  meniscus  corresponds  to  the  mark  on  the  stem 
of  the  pipet;  remove  the  pipet  from  the  flask  and  allow  the  solution 
to  flow  into  a  clean  150  cc.  beaker  and  to  drain  for  two  minutes, 
but  do  not  wash  out  with  water. 

Determination  of  Copper  by  Electrolysis.  To  one  of  the  so- 
lutions which  has  been  separated,  add  sufficient  ammonium  hy- 
droxide to  make  it  slightly  alkaline,  then  2  cc.  of  concentrated 
nitric  acid.  Ignite  and  weigh  accurately  a  clean  platinum  cath- 
ode, place  in  the  solution  and  add  water  enough  to  cover  the 
electrode.  Introduce  a  spiral  anode  and  connect  both  with  the 
terminals  of  a  storage  battery.  Change  the  resistance  in  the 
circuit  by  means  of  a  rheostat  until  a  current  of  0.5  ampere  if  a 
gauze  electrode  is  used,  or  of  0.05  ampere  if  a  foil  electrode  is 
used,  passes  thru  the  solution.  Allow  the  electrolysis  to  pro- 
ceed for  fifteen  minutes  after  the  solution  has  become  colorless, 
if  a  gauze  electrode  has  been  used,  or  for  one  hour  after  the 
solution  has  become  colorless,  if  a  foil  electrode  has  been  used. 
The  entire  time  necessary  should  be  about  ninety  minutes  and 
twelve  hours,  respectively. 

Place  a  small  beaker  containing  sufficient  water  to  cover  the 
cathode  on  the  bench  x[ear  the  solution  being  electrolyzed,  raise 
the  stand  supporting  the  electrodes  and,  without  disconnecting 
the  attached  wires,  plunge  the  electrodes  into  the  beaker  of  pure 
water.  Allow  the  current  to  pass  for  a  few  minutes,  rinse  the 
electrodes  by  rotating  the  beaker,  then  disconnect  the  cathode, 
remove  from  the  water,  allow  to  drain  and  absorb  as  much  of  the 
water  as  possible  by  bringing  into  contact  with  a  piece  of  filter 
paper.  Rinse  the  cathode  in  at  least  two  changes  of  95  per  cent 
alcohol,  absorb  the  excess  of  alcohol  by  means  of  filter  paper  and 
dry  for  a  few  minutes  at  a  temperature  of  about  50°,  which  can 


ANALYSIS  OF  BRASS  189 

be  done  by  holding  over  a  sand  bath  for  a  few  minutes;  then 
weigh  accurately,  and  calculate  the  percentage  of  copper  present. 

Determination  of  Zinc.  Evaporate  the  aqueous  washings  from 
the  cathode  to  a  small  bulk  and  transfer  both  the  washings  and 
the  residual  solution  to  a  300  cc.  beaker;  add  ammonium  hydroxide 
until  the  solution  is  neutral  to  litmus  paper,  heat  to  boiling,  add  10 
cc.  of  sodium  phosphate  solution  and  again  neutralize  the  solution 
very  carefully  with  either  dilute  ammonium  hydroxide  or  hydro- 
chloric acid,  as  may  be  found  necessary. 

Heat  the  solution  almost  to  the  boiling  point  and  keep  at  that 
temperature  for  fifteen  minutes,  that  is,  until  the  flocculent 
precipitate  which  separates  at  first  becomes  crystalline.  Set 
the  mixture  aside  for  half  an  hour  and  while  waiting,  prepare 
and  weigh  a  Gooch  crucible.  Filter  off  the  precipitate,  wash  free 
from  soluble  salts  with  pure  water,  dry,  ignite  gently  at  first  and 
then  at  a  bright  redness,  cool  and  weigh  accurately.  Calculate 
the  percentage  of  zinc  present  from  the  weight  of  zinc  pyro- 
phosphate  found. 

III.   QUESTIONS  AND  PROBLEMS.     SERIES  12 

1.  Would  it  be  desirable  to  vary  the  volume  of  sulfuric  a.cid  added  before 
evaporation  if  the  amount  of  sample  used  was  varied,  or  if  the  relative  amounts 
of  copper  and  zinc  in  the  sample  varied? 

2.  Calculate  by  means  of  Faraday's  law  the  time  theoretically  required  to 
precipitate  0.3  gm.  of  copper  with  a  current  of  0.5  ampere,  and  show  why  the 
calculation  has  but  little  significance  in  this  determination. 

v  3.  Explain  how  the  addition  of  sodium  hydrogen  phosphate  to  the  neutral 
solution  containing  zinc  and  ammonium  salts  may  increase  the  concentration 
of  the  hydrogen  ions  present. 

'  4.  Explain  the  advantage  of  starting  with  3  gm.  of  sample  and  using  a 
fractional  part  of  the  solution  for  the  determination  of  copper  and  zinc. 


CHAPTER  XXVII 

DETERMINATION   OF   SILICA  IN  A  HORNBLENDE 
I.  FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Methods  of  Decomposition.  Silicates  of  the  insoluble  class, 
such  as  the  hornblendes  and  the  great  majority  of  the  naturally- 
occurring  silicates,  must  be  decomposed  by  means  of  hydrofluoric 
acid,  or  changed  into  silicates  of  the  soluble  class  by  fusion  with 
certain  fluxes.  If  the  hydrofluoric  acid  method  is  employed  the 
decomposition  must  be  carried  out  in  vessels  of  platinum,  and  since 
the  silicon  present  forms  volatile  silicon  fluoride,  it  cannot  be  deter- 
mined unless  the  apparatus  has  a  form  which  makes  it  possible  to 
absorb  all  of  the  liberated  gas  in  an  appropriate  reagent.  Such  an 
apparatus  would  be  too  expensive  for  general  use. 

The  transformation  into  silicates  of  the  soluble  class  can  be 
effected  by  fusion  with  any  strongly  basic  reagent,  such  as  the 
hydroxides,  oxides  or  carbonates  of  metals  of  the  sodium  and 
calcium  group.  Such  fusions  must  necessarily  be  carried  out  in 
vessels  free  from  silicon;  a  platinum  crucible  is  to  be  preferred, 
but  one  of  silver  or  nickel  is  sometimes  used.  A  mixture  of  four 
parts  sodium  and  five  parts  potassium  carbonates,  which  melts 
at  685°  is  most  frequently  used;  it  does  not  attack  platinum 
appreciably.  As  these  reagents  usually  contain  appreciable  per- 
centages of  silica  it  becomes  necessary  to  determine  the  percentage 
present  and  apply  a  correction  to  the  final  result.  When  a  finely- 
powdered  sample  of  hornblende  is  heated  to  a  temperature  of  about 
600°  with  this  mixture,  silicates  and  aluminates  of  sodium  and 
potassium  are  produced  and  the  corresponding  amount  of  carbon 
dioxide  liberated. 

190 


DETERMINATION  OF  SILICA  IN  A  HORNBLENDE       191 

The  Dehydration  of  Silicic  Acid.  When  a  soluble  silicate  is 
treated  with  an  excess  of  hydrochloric  acid,  free  silicic  acid  and  the 
chlorides  of  all  the  metals  present  are  formed.  If  the  acid  used 
is  dilute  and  the  temperature  is  kept  low  the  silicic  acid  may 
remain  in  solution,  but  if  these  conditions  are  not  complied  with 
most  of  it  separates  as  a  gelatinous  colloid,  which  is  extremely 
difficult  to  filter.  When  the  mixture  is  evaporated  to  dryness  the 
silicic  acid  gradually  loses  water  and  assumes  a  fine,  powdery  form. 

Experience  shows  that  complete  conversion  of  the  silicic  acid 
into  an  insoluble  form  is  not  easily  effected.  Some  chemists  dry 
the  residue  from  evaporation  at  a  temperature  of  120°  for  a  half 
hour  or  more,  but  this  results  in  the  formation  of  compounds  of 
iron  an4  alumina  which  are  very  difficult  to  dissolve,  others  dry 
at  105°  or  evaporate  to  complete  dryness  on  the  water  bath  several 
times.  Two  evaporations  with  an  intermediate  filtration  of  the 
dehydrated  silicic  acid  are  more  effective  than  two  successive 
evaporations,  but  even  when  this  method  is  adopted  small  amounts 
of  silica  may  be  left  in  the  solution.  In  dissolving  the  soluble 
salts  from  the  residue  left  after  evaporation  either  cold  water  or 
hot  dilute  acid  should  be  used;  if  hot  water  alone  is  employed 
the  iron  and  aluminum  present  may  form  insoluble  basic  salts. 
Even  when  the  mixture  is  evaporated  on  the  water  bath  only,  the 
silica  obtained  may  contain  small  amounts  of  iron  and  aluminum, 
but  the  error  resulting  from  this  is  largely  counterbalanced  by  the 
error  from  incomplete  dehydration.  Where  the  highest  degree 
of  accuracy  is  demanded  it  becomes  necessary  to  volatilize  the 
silica  in  the  precipitate  by  treating.it  with  hydrofluoric  and  sul- 
furic  acids  in  a  platinum  crucible,  and  determining  the  impurities, 
representing  iron  and  aluminum  oxides,  remaining;  also,  to 
separate  the  silica,  which  has  remained  in  the  solution,  but  is 
subsequently  precipitated  with  the  iron  and  alumina.  These 
refinements  are  not  usually  considered  necessary  in  commercial 
work. 

The  ignition  of  a  silica  precipitate  requires  extreme  care  owing 


192  QUANTITATIVE  CHEMICAL  ANALYSIS 

to  its  fine,  powdery  nature.  If  the  paper  filter  used  is  heated  too 
rapidly,  and  especially  if  it  catches  fire  and  burns  at  the  mouth  of 
the  crucible,  appreciable  amounts  of  the  precipitate  may  be 
carried  off  by  the  air  currents  formed.  There  is  no  danger  of 
reducing  or  otherwise  changing  the  composition  of  the  precipitate, 
but  long-continued  ignition  at  the  highest  temperature  readily 
attainable  with  a  burner  is  necessary  to  completely  convert  the 
precipitate  into  the  dioxide. 

III.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Selection  and  Preparation  of  the  Sample.  Carefully  select 
from  the  roughly  crushed  sample  about  3  gm.  of  the  pure  mineral. 
Place  half  gram  portions  at  a  time  in  a  clean  agate  mortar  and  grind 
each  portion  until  the  resulting  powder  tends  to  form  a  compact 
thin  layer  on  the  side  of  the  mortar  and  no  longer  feels  gritty 
when  rubbed  between  the  fingers.  Place  a  perfectly  clean  100- 
mesh  sieve  over  a  piece  of  glazed  paper,  brush  the  powdered 
mineral  into  the  sieve  and  tap  it  until  all  of  the  fine  powder  has 
passed  thru  it.  Return  the  powder  left  on  the  sieve  to  the  mortar 
and  continue  grinding  and  sifting  until  all  of  it  has  passed  thru 
the  sieve.  Finally  transfer  the  powdered  mineral  into  a  clean,  dry, 
well-stoppered  weighing  tube. 

Fusion.  Weigh  out  in  a  platinum  crucible  of  at  least  10  cc. 
capacity  about  4  gm.  of  fusion  mixture.  Weigh  the  tube  contain- 
ing the  silicate  and  pour  from  it  into  the  crucible  about  0.7  gm. 
of  the  sample  and  again  weigh  accurately.  Thoroughly  mix  the 
silicate  with  the  fusion  mixture  by  the  use  of  a  platinum  spatula 
or  a  stirring  rod,  which  has  a  carefully  rounded  end,  then  brush 
from  the  latter  any  of  the  adhering  mixture  and  tap  the  crucible 
till  the  mixture  is  well  settled. 

Place  the  crucible  on  a  triangle  and  heat  it  with  a  low  flame 
for  about  five  minutes,  then  gradually  increase  the  temperature 
until  the  mass  begins  to  fuse  and  keep  at  this  point  until  carbon 
dioxide  is  no  longer  evolved.  The  crucible  should  be  kept  covered 


DETERMINATION  OF  SILICA  IN  A  HORNBLENDE       193 

to  avoid  loss  from  spattering  and  the  temperature  must  be  care- 
fully controlled  or  the  mixture  may  boil  over.  The  entire  fusion 
should  require  from  twenty  minutes  to  half  an  hour  and  should 
finally  yield  a  quiescent  mass  of  perfectly  sintered  but  only  par- 
tially fused  material. 

Decomposition.  Remove  the  crucible  from  the  triangle  by 
means  of  a  pair  of  forceps  while  still  hot,  and  by  carefully  tipping 
and  rotating  the  latter  cause  the  contents  to  solidify  as  a  layer 
around  its  inner  surface.  When  cold  place  the  crucible  on  its 
side  in  the  bottom  of  a  five-inch  casserole,  add  50  cc.  of  water, 
warm  and  stir  until  the  fused  mass  is  disintegrated  and  falls  out 
of  the  crucible,  then  remove  the  crucible  from  the  dish  with  the  aid 
of  a  glass  rod  and  wash  both  inner  and  outer  surfaces  thoroughly. 
Cover  the  dish  with  a  watch  glass  and  gradually  introduce  20  cc. 
of  hydrochloric  acid.  The  dish  should  now  contain  only  gelatinous 
silicic  acid  and  a  clear  yellow  solution.  If  sandy  or  gritty  particles 
are  present  the  decomposition  is  probably  incomplete  and  a  second 
sample  must  be  fused.  Sometimes  the  precipitated  silica  has  a 
reddish  color  owing  to  the  presence  of  difficultly  soluble  iron 
compounds,  which  usually  dissolve  on  digestion. 

Separation  of  Silica.  Place  the  dish  on  the  steam  bath  and 
evaporate  to  complete  dryness,  that  is,  till  powdery  dry.  The 
evaporation  may  be  made  more  rapidly  by  heating  on  a  sand 
bath,  or  over  a  gauze  placed  some  distance  above  the  flame  of 
the  burner  if  the  precipitate  is  kept  in  constant  motion  with  a 
stirring  rod.  Moisten  the  residue  with  about  10  cc.  of  concen- 
trated hydrochloric  acid  and  then  add  1  cc.  of  nitric  acid  and  50  cc. 
of  water,  and  digest  on  the  steam  bath  until  all  basic  salts  have 
been  decomposed  and  white  silicic  acid  only  remains. 

Filter  thru  a  9  cm.  filter  and  transfer  the  precipitate  to  the 
filter,  then  wash  twice  with  10  cc.  portions  of  cold  water.  Next 
transfer  the  filtrate  and  washings  which  may  still  contain  small 
amounts  of  silicic  acid  to  the  casserole  previously  used,  evaporate 
the  mixture  to  complete  dryness  on  the  steam  bath  and  keep  the 


194  QUANTITATIVE  CHEMICAL  ANALYSIS 

dry  residue  on  the  bath  one  half  hour  longer.  While  the  solution 
in  the  dish  is  evaporating  continue  to  wash  the  silica  precipitate 
until  the  washings  are  shown  to  be  free  from  chlorine,  receiving 
the  washings  in  a  clean  300  cc.  beaker. 

Treat  the  residue  from  the  second  evaporation  with  20  cc.  of 
dilute  hydrochloric  acid  and  digest  until  all  basic  salts  have  been 
decomposed,  add  50  cc.  of  water  and  then  filter  thru  a  fresh  9  cm. 
filter,  receiving  the  filtrate  in  the  beaker  containing  the  washings 
from  the  first  silica  precipitate.  Next  rub  the  entire  inner  surface 
of  the  dish  with  a  rubber-tipped  rod  until  the  adhering  precipitate 
has  been  loosened,  and  rinse  into  the  filter;  finally  wash  the  latter 
until  free  from  soluble  salts. 

Place  the  two  still  moist  filters  in  a  weighed  crucible  and  heat 
cautiously  over  a  wire  gauze  until  combustible  gases  are  no  longer 
given  off,  then  place  the  crucible  over  a  wire  triangle  and  gradually 
increase  the  temperature  until  the  paper  is  entirely  consumed; 
finally  ignite  over  a  blast  lamp,  or  Meker  burner  for  at  least 
twenty  minutes  and  weigh.  Repeat  the  ignition  till  the  weighings 
are  practically  constant. 

Determination  of  Silica  in  Reagents.  Weigh  out  10  gm.  of 
the  fusion  mixture  used  into  a  casserole,  cover  with  a  watch  glass 
and  cautiously  introduce  sufficient  dilute  hydrochloric  acid  to 
decompose  it.  Evaporate  to  complete  dryness  and  separate  the 
silica  as  in  the  analysis.  Calculate  the  weight  of  silica  in  the  weight 
of  fusion  mixture  used  in  the  analysis  and  subtract  from  the  weight 
of  precipitate  found.  Report  the  corrected  per  cent  of  silica 
present. 


SECTION   IV 
SOLUTION  AND  EXTRACTION   PROCESSES 


CHAPTER  XXVIII 

GENERAL  FEATURES  OF  SOLUTION  AND  EXTRACTION  PROCESSES 

Solution  Processes  Which  Depend  Upon  the  Physical  Action 
of  the  Solvent.  These  processes  depend  upon  the  differential 
action  of  liquids  on  mixtures  composed  of  two  or  more  solids. 
The  simplest  possible  example  is  one  in  which  the  mixture  consists 
of  two  distinct  solid  phases,  each  phase  representing  a  single 
component,  one  of  which  is  much  more  soluble  in  some  particular 
liquid  than  the  other.  If  the  difference  in  solubility  is  sufficiently 
large,  and  if  the  mixture  is  so  finely  divided  that  every  particle 
of  the  more  soluble  constituent  is  exposed  to  the  action  of  the 
solvent,  treatment  of  the  mixture  with  a  sufficient  amount  of  the 
solvent  at  once  yields  a  liquid  phase  which  contains  all  of  the  more 
soluble  component,  and  a  residual  solid  phase  composed  of  the  less 
soluble  component.  The  action  concerned  is  the  converse  of  that 
of  precipitation  processes,  but  the  rate  at  which  equilibrium  is 
attained  when  a  liquid  acts  upon  a  solid  is  slower  than  when  a 
precipitate  is  formed  in  a  liquid,  and  altho  the  theory  of  the  two 
classes  of  methods  is  essentially  the  same  the  methods  by  which 
they  are  carried  out  are  decidedly  different. 

The  ideal  method  of  making  such  a  separation  would  be  to  use 
only  sufficient  solvent  to  bring  into  solution  all  of  the  more  soluble 
component,  but  such  a  method  of  procedure  would  not  be  practi- 
cable owing  to  the  slowness  with  which  solution  of  the  last  particles 
of  the  more  soluble  constituent  is  effected,  and  the  adherence  of 
some  of  the  liquid  to  the  solid  phase,  which  makes  it  necessary  to 
wash  the  residue  with  further  quantities  of  the  solvent.  The 
general  theory  of  the  method  actually  used  in  carrying  out  such 
processes  is  similar  to  that  elaborated  in  Chapter  XVII  for  the 

195 


196  QUANTITATIVE  CHEMICAL  ANALYSIS 

washing  of  precipitates.  The  comparative  rates  at  which  the 
two  components  pass  into  solution,  the  effect  of  one  component 
upon  the  solubility  of  the  other,  the  size  of  the  particles  of  which 
the  mixture  is  composed,  and  the  relative  amounts  of  the  two  com- 
ponents, all  affect  the  accuracy  and  efficiency  of  such  processes. 
An  ideally  perfected  method  for  making  a  separation  of  this  kind 
would  prescribe  the  weight  of  the  mixture  to  be  used,  the  compo- 
sition and  amount  of  the  solvent  to  be.  used  for  each  treatment, 
the  number  of  treatments,  and  the  length  of  time  allowed  for 
each  treatment.  These  details  are  best  determined  empirically, 
that  is,  by  quantitative  experiments  with  mixtures  of  known  com- 
position; in  many  of  the  processes  largely  used  these  details  have 
only  been  determined  very  roughly. 

In  discussing  the  theory  of  this  class  of  methods  it  is  assumed 
that  the  two  components  of  the  mixture  exist  as  distinct  and 
separate  solid  phases.  Some  doubt  should  always  be  entertained 
as  to  whether  the  method  can  be  successfully  applied  to  the 
separation  of  a  mixture  of  isomorphous  substances  which  has 
separated  from  a  solution,  or  has  resulted  from  the  solidification 
of  a  molten  magma;  that  is,  wherever  the  presence  of  solid 
solutions  is  possible.  A  solvent  which  readily  dissolves  one  of  the 
two  components  of  a  solid  solution  will  often,  especially  where 
the  less  soluble  component  is  present  in  relatively  small  amounts, 
readily  disintegrate  and  decompose  such  a  mixture,  but  not  in  all 
cases. 

This  class  of  methods  is  of  especial  use  in  the  separation  of  those 
elements  all  of  whose  compounds  are  largely  soluble  in  aqueous 
solvents,  and  which,  therefore,  cannot  be  separated  by  the  use 
of  precipitation  methods.  In  using  them  it  is  often  necessary 
to  convert  the  substance  to  be  separated  into  those  particular 
compounds  which  possess  the  necessary  differences  in  solubility 
in  some  particular  solvent. 

Solution  Processes  which  Depend  Upon  the  Chemical  Action 
of  the  Solvent.  Processes  in  which  the  action  of  the  solvent  is 


FEATURES  OF  SOLUTION  AND  EXTRACTION  PROCESSES     197 

chemical  as  well  as  physical  are  also  extensively  used.  In  all  such 
cases  two  sets  of  equilibria  must  be  considered.  The  equilibrium 
resulting  from  the  contact  of  solvent  and  one  of  the  solids  must 
result  in  the  formation  of  a  single  liquid  phase,  that  is,  must  involve 
a  change  from  heterogeneous  to  homogeneous  equilibrium;  that 
resulting  from  contact  of  the  solvent  with  the  other  solid  must 
involve  maintenance  of  the  original  condition. 

As  in  the  case  of  processes  in  which  the  action  of  the  solvent 
is  purely  physical  the  formation  of  solid  solutions  often  makes  it 
impossible  to  effect  separations  which  could  otherwise  be  easily 
made.  The  chemical  as  well  as  the  physical  properties  of  solid 
solutions  are  specific  properties  of  the  mixture,  and  vary  with  the 
comparative  amounts  of  the  two  components  actually  present. 
Thus,  altho  metallic  silver  is  readily  changed  into  a  solution  of 
silver  nitrate  by  treatment  with  a  dilute  solution  of  nitric  acid, 
it  is  not  possible  to  separate  silver  from  gold  in  an  alloy  which 
contains  more  than  30  per  cent  of  gold  because  the  two  metals 
form  a  continuous  series  of  solid  solutions. 

Extraction  Processes.  Further  difficulties  are  encountered  in 
applying  this  class  of  methods  to  the  analysis  of  certain  classes  of 
materials  such  as  plant  and  animal  tissues.  In  such  substances 
the  soluble  constituent  may  be  diffused  thru  or  surrounded  by 
cell  walls,  which  act  as  semi-permeable  membranes  and  prevent 
diffusion  of  the  solvent.  The  difficulty  can  be  overcome  to  some 
extent  by  mechanical  disintegration  and  crushing  of  the  sample, 
but  even  where  the  sample  is  reduced  to  a  very  fine  powder  it  is 
often  necessary  to  treat  it  with  the  solvent  for  many  hours.  To 
successfully  carry  out  such  a  separation  by  supporting  the  mixture 
on  a  filter  and  washing  with  the  solvent  is  impracticable,  as  it 
necessitates  the  use  of  very  large  amounts  of  the  solvent,  which  is 
often  an  expensive  reagent,  and  demands  a  large  amount  of  time, 
and  care  from  the  analyst.  It  is  then  necessary  to  " extract'7  the 
substance  in  an  apparatus  of  especial  construction,  which  is  known 
as  an  "  extraction  apparatus." 


198 


QUANTITATIVE  CHEMICAL  ANALYSIS 


Extraction  methods  are  of  especial  importance  in  the  analysis  of 
mixtures  containing  organic  compounds  for,  owing  to  the  low  tem- 
peratures employed  in  carrying  on  the  process,  and  the  slight 
activity  of  the  solvents  which  are  most  frequently  used,  the  prob- 
ability of  decomposing  these  compounds  is  reduced 
to  a  minimum.  They  are  universally  used  in  the 
analysis  of  substances  of  animal  or  vegetable 
origin,  of  all  classes  of  explosives,  and  of  asphalt 
paving  materials. 

Apparatus  for  Continuous  Extraction.  The 
conditions  necessary  for  the  rapid  and  complete 
extraction  of  any  solid  substance  are  most  readily 
and  effectively  maintained  by  boiling  the  solvent 
in  a  small  flask  attached  to  an  inverted  condenser 
so  arranged  that  the  condensed  solvent  is  made 
to  fall  into,  and  drip  thru,  a  filter  containing 
the  substance  to  be  extracted.  An  apparatus  of 
this  kind  is  represented  in  Fig.  40.  It  consists  of 
a  wide-mouthed  flask  A  of  about  125  cc.  capacity, 
which  contains  the  boiling  solvent;  an  extraction 
tube  B,  which  supports  the  " extraction  shell" 
C  containing  the  sample;  and  the  condenser  D. 
The  vapor  of  the  boiling  solvent  passes  thru 
the  side  tube  E  into  the  condenser,  and  after  con- 
densation falls  into  the  extraction  shell,  where 
it  comes  into  contact  with  the  sample,  passes 
thru  the  shell,  and  falls  back  into  the  flask. 
Fresh  portions  of  the  pure  warm  solvent  are  thus 
Fig.  40.  —  Contin-  continuously  brought  into  contact  with  and  made 

10    paSS    thm    the    She11    and    its    contents>    and 
gradually  wash  out  those  constituents  which  are 

soluble.  As  these  are  usually  much  less  vqjatile  than  the  solvents 
used  they  accumulate  in  the  flask  in  the  form  of  a  solution,  whose 
concentration  increases  as  the  process  of  extraction  progresses. 


FEATURES  OF  SOLUTION  AND  EXTRACTION  PROCESSES     199 


A  more  compact,  and  in  some  respects  more  desirable,  apparatus 
is  the  one  devised  by  Wiley,  which  is  represented  in  Fig.  41.  The 
substance  to  be  extracted  is  here  placed  in  a  Gooch  crucible  C, 
which  is  suspended  from  the  very  efficient  metallic 
condenser  B ;  both  crucible  and  condenser  are  con- 
tained in  the  tube  A,  which  holds  the  boiling  sol- 
vent. Both  figures  represent  forms  of  extraction 
apparatus  in  which  the  distilled  and  condenser 
solvent  is  made  to  leach  the  solvent  continuously 
and  are  therefore  designated  as  "  continuous." 
Apparatus  for  Intermittent  Extraction.  Another 
type  of  apparatus,  of  which  there 
are  also  many  forms,  acts  intermit- 
tently. It  is  represented  by  the 
Soxhlet  apparatus  shown  in  Fig.  42 
and  differs  from  the  apparatus  al- 
ready described  in  the  form  of  the 
extraction  tube.  This  is  closed  at  Fig.  41.— Wiley 
the  point  A,  but  is  provided  with  a 
side  tube  B  thru  which  the  vaporized 


B 


Extraction 
Apparatus 


f 


solvent  passes  into  the  condenser,  and  a  siphon  tube 
C  thru  which  the  solution,  which  accumulates  in  the 
extraction  tube,  runs  back  into  the  flask  as  soon  as 
it  reaches  the  level  D.     The  action  of  this  type  of 
apparatus  is  distinguished  by  the  fact  that  a  large 
volume  of  the  solvent  remains  in  contact  with  the 
sample  for  a  relatively  long  time;  since,  however, 
there  is  little  circulation,  that  portion  of  the  solvent 
Fig.  42.— Soxh-  m  immediate  contact  with  the  sample  soon  attains 
tion  Tube*0"  a  fairly  large  deSree  of  concentration  with  respect 
to  the  soluble  compound,  which  delays  further  solu- 
tion.    By  using  the  method  of  reasoning  already  employed  in 
discussing  the  theory  of  washing  precipitates  it  is  easy  to  show  that 
the  continuous  type  of  apparatus  should  be  more  efficient  than  the 


200 


QUANTITATIVE  CHEMICAL  ANALYSIS 


intermittent,  and  a  comparison  of  the  efficiency  of  the  two  types 
under  similar  conditions  confirms  the  accuracy  of  this  conclusion; 
furthermore,  the  amount  of  solvent  required  to  operate  the  contin- 
uous type  of  apparatus  is  much  less  than  that  required  for  the 
intermittent. 

Construction  of  Joints  to  Apparatus.  The  sol- 
vents which  are  most  extensively  used  are  alcohol, 
ethyl  ether,  petroleum  spirit,  chloroform,  carbon 
disulphide  and  carbon  tetrachloride.  All  of  these 
are  extremely  volatile,  and  all  except  chloroform 
are  extremely  inflammable.  It  is  essential,  there- 
fore, that  all  joints  of  the  apparatus  should  be 
tight,  and  that  the  condensation  of  the  vaporized 
solvent  should  be  as  perfect  as  possible.  Rubber 
dissolves  in  all  of  the  solvents  named  except  alcohol 
to  some  extent,  and  such  media  as  wax  or  paraffin, 
which  are  sometimes  used  to  remedy  the  deficiencies 
of  cork  stoppers,  are  also  dissolved  by  these  sol- 
vents appreciably.  It  is  desirable,  therefore,  to 
use  an  apparatus,  like  the  Wiley  apparatus  already 
described,  which  has  no  joints,  or  one  which  is 
made  entirely  of  glass;  if  the  latter  alternative  is 
adopted  the  ground-glass  joints  which  become  neces- 
sary must  be  very  carefully  made,  and  they  are 
both  expensive  and  easily  broken. 

Still  another  alternative  involves  the  use  of  an 
apparatus,   such  as  the  Knorr  apparatus   repre- 
Fig.43.  —  Knorr  sented  in  Fig.  43  or  the  Ames  apparatus  repre- 

S6nted  in  Fig*  44'  in  which  the  °nly  J°int  which 
is  exposed  to  the  action  of  the  solvent  is  provided 

with  a  "  mercury  seal."  In  both  forms  the  flask  in  which  the  sol- 
vent is  made  to  boil  is  provided  with  a  groove  into  which  the  tube 
B  fits  loosely,  the  intervening  space  being  filled  with  sufficient 
mercury  to  prevent  the  escape  of  any  of  the  vaporized  solvent. 


FEATURES  OF  SOLUTION  AND  EXTRACTION  PROCESSES     201 


Where  these  more  elaborate  and  therefore  more  expensive  types 
of  apparatus  are  not  available,  recourse  must  be  had  to  simpler 
forms,  in  which  the  joints  are  made  by  means  of  cork  stoppers. 
These  can  usually  be  made  to  give  tight  joints  if  corks  of  good 
quality  and  large  size  are  chosen,  boiled  in 
water  for  an  hour,  and  while  still  hot  and  plastic 
forced  into  the  opening  to  be  closed,  and  then 
allowed  to  dry  in  this  position;  they  should  be 
bored  to  fit  the  necessary  connections  when 
dry  and  cold. 

Methods  of  Heating  the  Apparatus  During 
Extraction.  Since  the  rate  at  which  the 
soluble  constituent  is  leached  out  depends  upon 
the  rate  at  which  the  solvent  circulates  thru 
the  extraction  shell,  it  is  desirable  to  heat  the 
solvent  by  means  of  a  device  which  causes  it 
to  boil  vigorously  and  steadily,  that  is,  with- 
out danger  of  boiling  over.  Direct  heating  of 
the  flask  with  a  flame  is  always  to  be  avoided, 
since  it  is  hard  to  regulate  the  rate  of  boil- 
ing, and  if  the  flask*  cracks  or  if  the  joints  of 
the  apparatus  are  not  tight  the  flame  may  set 
fire  to  the  escaping  solvent.  The  use  of  a 
water  bath  is  more  satisfactory  but  has  some 
disadvantages.  An  electric  hot  plate  or  an 
air  bath  heated  by  a  current  passing  thru 
resistance  wires  or  incandescent  lamps  is  to  be  Fig.  44.— Ames  Ex- 
preferred  to  all  other  devices,  since  the  danger 
from  fire  is  reduced  to  a  minimum  and  any  desired  temperature 
can  be  maintained  by  the  use  of  proper  resistances  in  the  circuit. 

Determination  of  the  Separated  Constituent.  The  weight  of 
the  constituent  dissolved  from  the  sample  can  be  determined  from 
the  difference  between  the  weight  of  the  sample  and  that  of  the 
solid  residue  left,  or  if  the  substance  extracted  is  not  appreciably 


202  QUANTITATIVE  CHEMICAL  ANALYSIS 

volatile,  the  solvent  can  be  distilled  off  from  the  solution  and  the 
desired  weight  determined  directly.  Where  the  former  method  is 
used  difficulties  may  arise  from  the  hygroscopic  character  of  the 
residue  or  of  the  extraction  shell  used.  The  alternative  method 
of  procedure  is  always  to  be  preferred  unless  the  dissolved  con- 
stituent is  so  volatile  that  appreciable  amounts  of  it  are  carried 
over  with  the  solvent  during  the  distillation. 

Multiple  Extraction  Apparatus.  Although  the  actual  labor 
involved  in  making  a  determination  by  an  extraction  method  is 
small,  it  is  often  necessary  to  extract  a  sample  for  several  hours, 
and  where  a  large  number  of  such  determinations  have  to  be  made 
it  becomes  almost  imperative  to  operate  a  number  of  such  appara- 
tus simultaneously.  Many  forms  of  multiple  extraction  apparatus 
in  which  a  series  of  extraction  units  are  supported  on  a  common 
frame,  and  supplied  with  a  common  source  of  heat  and  condenser 
water  are  in  use.  An  apparatus*  consisting  of  five  such  units  is 
represented  in  Fig.  45;  this  apparatus  is  also  provided  with  a 
common  device  for  the  distillation  and  condensation  of  the  solvent 
after  the  extraction  has  been  completed. 

The  heating  device  here  used  consists  of  five  electrically-heated 
iron  plates  supported  on  a  wooden  base,  but  separated  from  it  by 
a  sheet  of  asbestos.  The  edge  of  each  plate  is  surrounded  by  a 
strip  of  mica,  which  prevents  the  plate  from  short-circuiting  the 
resistance  wire  by  which  it  is  heated,  but  does  not  prevent  the 
transfer  of  heat  to  it.  A  nichrome  wire  0.01  mm.  in  diameter 
passes  thru  a  series  of  cleats  fastened  to  the  bed  and  makes  three 
complete  turns  around,  and  in  close  contact  with,  the  edge  of  each 
of  the  five  plates;  this  wire  is  connected  directly  with  the  ter- 
minals of  a  110-volt  alternating  current  by  means  of  a  switch. 
The  wire  offers  a.  resistance  of  75  ohms  and  consumes  1.5  amperes. 

The  condenser  used  during  distillation  consists  of  a  worm  of 
block  tin  tubing  supported  in  and  surrounded  by  .a  cylindrical 

*  Further  details  concerning  the  construction  of  this  apparatus  will  be 
found  in  the  Jour,  of  Ind.  and  Eng.  Chem.,  4,  302  (1912). 


FEATURES  OF  SOLUTION  AND  EXTRACTION  PROCESSES     203 


Fig.  45. — .Plan  of  a  Multiple  Extraction  Apparatus 


204  QUANTITATIVE  CHEMICAL  ANALYSIS 

copper  vessel  thru  which  the  waste  water  from  the  other  series  of 
condensers  can  be  made  to  flow.  One  end  of  the  worm  passes 
thru  the  bottom  of  the  copper  vessel,  the  other  is  prolonged  and 
supported  in  a  position  slightly  inclined  to  the  horizontal  on  a 
strip  of  wood  fastened  to  the  back  of  the  frame  of  the  apparatus. 
The  prolonged  end  is  provided  with  five  vertical  branches  placed 
at  points  opposite  to  the  centers  of  the  five  heating  plates.  Con- 
nection can  be  easily  established  between  any  of  the  flasks  resting 
on  one  of  the  plates  and  the  lateral  opposite  it  by  means  of  a  glass 
tube. 


CHAPTER  XXIX 

DETERMINATION  OF   POTASSIUM  IN  COMMERCIAL  POTASSIUM 

SULFATE 

I.   FACTS  UPON  WHICH  THE  METHOD  Is  BASED 

Composition  of  Samples.  This  salt  is  largely  used  as  a  ferti- 
lizer and  its  commercial  value  is  proportional  to  the  percentage  of 
potassium,  usually  reported  as  K2O,  which  it  contains.  In  addi- 
tion to  sulfate  of  potassium  it  contains  sulfates  and  chlorides  of 
sodium  and  magnesium. 

Choice  of  Method.  With  the  exception  of  a  complex  nitrite, 
which  has  the  formula  KNa2Co(N02)6,  the  compounds  of  potassium 
are  too  soluble  in  water  to  make  it  possible  to  determine  this 
element  by  a  precipitation  process.  The  two  methods,  which 
have  been  most  largely  used  up  to  the  present  time,  involve 
conversion  of  the  element  into  the  perchlorate  (KC104)  or  chloro- 
platinate  (K2PtCl6)  in  a  solid  form,  and  elimination  of  all  of  the 
other  salts  present  in  the  mixture  thus  obtained,  by  treating  it 
with  certain  solvents,  that  is,  by  methods  which  are  essentially 
solution  processes.  Of  the  three  methods  suggested  the  chloro- 
platinate  method  is  to  be  preferred,  especially  where  the  amount 
of  potassium  present  is  small,  on  account  of  the  large  molecular 
weight  of  the  compound  finally  separated  and  weighed,  and  also 
because  the  details  of  the  method  have  been  carefully  worked  out. 
Altho  the  reagent  used  is  very  expensive  the  platinum  can  be 
easily  recovered  after  use  and  reconverted  into  a  further  quantity 
of  reagent. 

Formation  of  Potassium  Chloroplatinate.  Solutions  contain- 
ing mixtures  of  potassium  and  sodium  chlorides  are  completely 
converted  into  K2PtCl6  and  Na2PtCl6-6  H20  respectively,  by 
evaporating  almost  to  dryness  with  the  theoretically  required 

205 


206  QUANTITATIVE   CHEMICAL  ANALYSIS 

amount  of  chloroplatinic  acid.  The  potassium  salt  separates  in 
well-formed  octahedra  belonging  to  the  regular  system;  the 
sodium  salt  in  plates  belonging  to  the  triclinic  system.  The  two 
compounds  do  not  form  double  compounds  nor  solid  solutions 
with  each  other,  nor  with  the  chlorides  of  sodium,  potassium, 
platinum  or  magnesium.  The  sulfate  of  potassium  is  readily 
changed  into  the  chloroplatinate  by  the  same  treatment,  but  the 
sulfate  of  sodium  is  not  so  readily  changed  into  the  corresponding 
sodium  compound.  The  reagent  used  for  this  purpose  should  be 
of  known  strength  and  of  high  concentration  if  economy  in  its  use 
and  in  the  time  needed  for  the  evaporation  is  to  be  attained.  A 
solution  which  contains  H2PtCl6  equivalent  to  0.1  gm.  of  Pt  per 
cc.  is  a  suitable  one  to  employ. 

Properties  of  Potassium  Chloroplatinate.  At  a  temperature 
of  20°  one  part  of  this  compound  requires  about  98  parts  of  water, 
or  26,400  of  80  per  cent  alcohol,  or  42,600  of  absolute  alcohol  for 
complete  solution.  Ammonium  chloroplatinate,  which  may  be 
formed  by  the  absorption  of  ammonium  hydroxide  from  the 
atmosphere  of  the  laboratory,  is  also  extremely  insoluble  in  these 
reagents.  Both  the  hydrated  and  anhydrous  sodium  chloro- 
platinate and  chloroplatinic  acid  are  readily  soluble  in  80  per  cent 
alcohol,  but  the  chlorides  and  sulfates  of  sodium,  potassium  and 
magnesium  are  but  slightly  soluble  in  this  reagent. 

When  made  to  separate  by  the  evaporation  of  moderately  dilute 
solutions,  potassium  chloroplatinate  is  coarsely  crystalline  and  does 
not  contain  either  combined  or  occluded  water.  It  can  be  dried 
at  a  temperature  of  135°  without  danger  of  decomposition  or 
volatilization;  at  higher  temperatures  it  is  slowly  decomposed 
into  potassium  chloride,  chlorine  and  metallic  platinum;  it  is  not 
appreciably  hygroscopic. 

Development  of  the  Lindo-Gladding  Method.  In  1881 
Lindo*  showed  that  potassium  could  be  determined  in  solutions 

*  Chemical  News,  44,  77,  86,  97, 129  (1881),  Bull.  7,  Division  of  Chem.  U.  S. 
Dept.  of  Agriculture. 


POTASSIUM  IN  COMMERCIAL  POTASSIUM  SULFATE     207 

containing  chlorides  of  sodium  and  potassium  by  evaporating  to 
dryness  with  sufficient  chloroplatinic  acid  to  convert  both  elements 
into  chloroplatinates,  leaching  out  the  sodium  salt  with  strong 
alcohol  and  weighing  the  residual  potassium  salt.  The  method 
could  not  be  used  when  S04  ions  were  present  owing  to  the  in- 
solubility of  sodium  sulfate  in  alcohol  and  altho  this  ion  could  be 
removed  by  the  use  of  barium  chloride,  and  the  excess  of  barium 
added  could  be  removed  by  the  use  of  ammonium  carbonate  this 
procedure  greatly  increased  the  length  and  difficulties  of  the 
method.  In  order  to  avoid  these  difficulties  Gladding  modified 
the  method  by  washing  the  mixture  first  obtained  with  sufficient 
alcohol  to  remove  all  of  the  sodium  chloroplatinate  and  chloro- 
platinic acid,  and  then  with  sufficient  ammonium  chloride  solution 
to  remove  the  sodium  sulfate.  This  modification  made  it  possible 
to  apply  the  method  to  substances  containing  organic  matter  and 
ammonium  salts,  for,  by  evaporating  with  a  slight  excess  of  sulfuric 
acid  and  igniting  gently,  both  classes  of  substances  could  be 
expelled  without  loss  of  potassium.  It  also  made  it  possible  to 
apply  the  method  to  substances  containing  magnesium  salts  as 
they  are  readily  dissolved  by  solutions  of  ammonium  chloride. 
The  slight  solubility  of  potassium  chloroplatinate  in  the  solution 
of  ammonium  chloride  used  was  reduced  to  zero  by  saturating  it 
with  potassium  chloroplatinate  before  use. 

The  method  has  been  investigated  by  the  Official  Association  of 
Agricultural  Chemists  and  the  exact  details  of  the  best  method  of 
procedure  as  applied  to  different  classes  of  substances  formulated. 
The  outline  given  below  is  the  official  method*  as  applied  to 
commercial  potassium  sulfate. 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Preparation  of  Solution.     Weigh  out  10  gm.  of  the  sample  into 
a  500  cc.  beaker,  add  300  cc.  of  water,  boil  for  a  few  minutes,  then 
transfer  to  a  500  cc.  graduated  flask.     Allow  to  cool,  dilute  to 
*  Bull.  107,  Bureau  of  Chemistry,  U.  S.  Dept.  of  Agriculture. 


208  QUANTITATIVE  CHEMICAL  ANALYSIS 

exactly  500  cc.,  mix  thoroughly,  filter  about  300  cc.  through  a  dry 
filter  and  preserve  in  a  stoppered  flask. 

Separation  of  Potassium.  Measure  out  25  cc.  of  the  solution 
by  means  of  a  pipet,  add  an  equal  volume  of  water,  acidify  with  a 
few  drops  of  hydrochloric  acid,  add  10  cc.  of  chloroplatinic  acid 
(1  cc.  =  0.1  gm.  Pt)  and  evaporate  on  the  water  bath  almost  to 
dryness.  Remove  from  the  bath  and  add  25  cc.  of  80  per  cent 
alcohol,  stir  the  mixture  with  a  rod  and  break  up  any  large  masses, 
and  after  about  five  minutes  decant  off  the  clear  liquid  thru  a 
weighed  Gooch  or  alundum  filtering  crucible.  Treat  the  residue 
with  three  10  cc.  portions  of  80  per  cent  alcohol,  stirring  the 
mixture  for  several  minutes  after  each  addition  and  decanting  as 
before.  The  last  addition  should  remain  colorless;  if  it  acquires 
even  a  faint  yellow  color  continue  the  washing.  Finally  transfer 
the  residue  to  the  filter  by  means  of  a  stream  of  alcohol  from  a 
wash  bottle. 

Wash  the  residue  on  the  filter  five  times  with  25  cc.  portions  of 
ammonium  chloride  wash  solution,*  then  with  three  10  cc.  portions 
of  80  per  cent  alcohol.  Dry  the  crucible  for  a  half  hour  at  100° 
and  weigh  accurately.  Calculate  and  report  the  percentage  of 
potassium  as  K20  present.  Save  both  the  precipitate  in  the 
crucible  and  the  filtrate  and  washings  for  the  recovery  of  the 
platinum  present. 

III.   QUESTIONS  AND  PROBLEMS.    SERIES  13 

1.  How  much  larger  percentage  error  is  involved  in  determining  potassium 
when  separated  as  KC1O4  than  when  separated  as  K2PtCl6,  assuming  that 
the  sample  contained  2  per  cent  of  K,  that  one-half  gram  was  used  and  that 
an  error  of  0.1  mg.  was  made  in  weighing  both  compounds? 

2.  What  is  the  maximum  error  from  solubility  in  the  determination  of 
K2O  in  a  substance  which  contains  20  per  cent,  assuming  that  all  of  the  details 
outlined  above  are  followed? 

*  Prepared  by  dissolving  100  gm.  of  ammonium  chloride  in  500  cc.  of  water, 
adding  from  5  to  10  gm.  of  pulverized  potassium  chloroplatinate  and  shaking 
at  intervals  for  from  six  to  eight  hours.  Allow  this  mixture  to  settle  over  night, 
then  filter.  The  residue  may  be  used  for  the  preparation  of  more  solution. 


POTASSIUM  IN  COMMERCIAL  POTASSIUM  SULFATE     209 

3.  Why  is  it  desirable  to  evaporate  on  a  water  baih  after  adding  the  H2PtCl6? 
Why  is  it  necessary  to  wash  out  all  Na2PtCl6  and  H2PtCl6  before  washing 
with  ammonium  chloride?     What  might  happen  if  the  mixture  was  heated 
after  alcohol  was  added?     Why  is  it  desirable  to  avoid  changes  in  temperature 
while  washing  with  the  (NH4)C1  solution? 

4.  What  modification  of  the  method  outlined  would  be  necessary  if  the 
sodium  and  potassium  were  present  as  nitrates  or  phosphates  respectively? 

5.  Outline  a  method  for  reconverting  the  platinum  saved  from  the  deter- 
mination into 


XXX 

DETERMINATION   OF  CRUDE  FAT  IN  PEANUTS 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Chemical  Nature  of  Fats  and  Oils.  In  the  analysis  of  foods 
the  different  constituents  are  classified  and  determined  with 
reference  to  the  function  they  perform  in  the  nutrition  of  the 
animal  body.  One  of  the  most  important  of  these  groups  consists 
of  fats  and  oils;  it  includes  a  very  large  number  of  organic  com- 
pounds, which  are  analogous  to  inorganic  salts,  in  that  they  rep- 
resent combinations  of  certain  organic  acids  and  glycerine,  which 
acts  as  a  trivalent  base.  The  most  important  are  olein,  palmatin 
and  stearine,  which  represent  normal  salts  of  oleic  (CnHasCOOH), 
palmitic  (Ci5H3iCOOH)  and  stearic  (Ci7H35COOH)  acids,  respec- 
tively. These  compounds  are  not  appreciably  hygroscopic  and 
do  not  absorb  oxygen  from  the  air,  but  the  "drying  oils/7  which 
are  obtained  when  flax  and  certain  other  seeds  are  extracted  con- 
tain linoleic  acid  (Ci7H3iCOOH),  and  since  this  compound  rapidly 
absorbs  oxygen  from  the  air  such  oils  are  difficult  to  weigh  accu- 
rately, j 

Meaning  of  "Crude  Fat."  All  of  the  compounds  referred  to 
above  are  distinguished  by  their  extreme  insolubility  in  water, 
and  very  slight  solubility  in  alcohol;  also  by  the  readiness  with 
which  they  are  dissolved  by  ethyl  ether,  petroleum  spirit,  carbon 
disulfide  and  carbon  tetrachloride.  The  remaining  constituents 
of  most  food  materials  are  not  appreciably  soluble  in  the  four 
solvents  last  named.  Many  classes  of  food  materials  contain 
small  amounts  of  other  substances  such  as  wax,  resin,  chlorophyll 
and  various  coloring  matters,  which  are  also  more  or  less  soluble 

210 


DETERMINATION  OF  CRUDE  FAT  IN  PEANUTS        211 

in  these  solvents,  especially  in  ethyl  ether.  Long-established 
custom  has  led  to  the  use  of  dry  ethyl  ether  for  the  determina- 
tion of  this  group  of  food  constituents.  Since  the  results  obtained 
by  extracting  a  material  with  ether  may  include  small  amounts 
of  substances  other  than  fat  the  result  should  always  be  designated 
as  "crude  fat"  or  "ether  extract." 

Purification  of  Ether.  Unless  especially  purified  ether  con- 
tains both  alcohol  and  water,  and  is  then  capable  of  dissolving 
appreciable  amounts  of  certain  sugars  and  other  compounds 
which  are  not  true  fats.  The  alcohol  can  be  removed  by  shaking 
the  solvent  with  water  and  allowing  the  mixture  to  stand  until  it 
separates  into  two  layers.  The  upper  ethereal  layer  is  then  re- 
moved and  the  large  amount  of  water  which  it  contains  separated 
by  adding  solid  calcium  chloride,  and  allowing  the  resulting 
aqueous  solution  of  calcium  chloride  to  separate  out;  the  residual 
ether  is  then  made  anhydrous  by. adding  metallic  sodium  and 
distilling.  The  purified  solvent  should  boil  at  35°.  From  35  to 
50  cc.  are  needed  for  each  extraction  where  the  continuous  type 
of  apparatus  is  used,  but  nearly  25  cc.,  which  can  be  again  used 
without  further  treatment,  should  be  recovered  when  it  is  distilled 
from  the  fat. 

Composition  of  Peanuts.  The  seeds  of  the  peanut  contain 
from  40  to  50  per  cent  of  substances  soluble  in  ether,  nearly  all  of 
which  are  true  fats.  At  least  80  per  cent  of  the  ether-soluble 
substances  is  tri-olein  and  the  remainder  is  made  up  of  the 
glyce^ides  of  stearic,  arachidic  (Ci9H39COOH)  and  lignoceric 
(C23H47COOH)  acids.  None  of  these  substances  absorb  oxygen 
from  the  air  at  an  appreciable  rate  and  hence  no  difficulty  is 
experienced  in  weighing  the  crude  fat  separated  directly.  On  the 
other  hand,  the  cellulose-containing  residue,  which  remains  after 
extraction,  is  appreciably  hygroscopic. 

Conditions  Necessary  for  Complete  Extraction.  Ether  pene- 
trates cellular  tissue  even  when  dry  but  slowly,  and  still  more 
slowly  when  the  tissue  is  moist.  If  the  sample  contains  much 


212  QUANTITATIVE  CHEMICAL  ANALYSIS 

moisture  it  is  slowly  taken  up  by  the  dry  ether  used,  and  gradually 
accumulates  in  the  ethereal  solution.  Since  the  water  cannot  be 
easily  distilled  off  from  the  crude  fat  without  using  an  undesirably 
high  temperature  an  appreciable  error  may  result  if  the  sample  is 
not  dried  before  it  is  extracted. 

The  large  amount  and  liquid  character  of  the  fat  present  makes 
it  impossible  to  grind  these  seeds  in  a  mill,  or  to  pass  the  ground 
pulp  through  a  sieve.  They  can  be  crushed  to  a  sticky  mass  in 
an  agate  mortar  but  this  will  still  contain  small  lumps  unless 
great  care  is  taken.  (The  pulp  can  be  completely  dehydrated  by 
drying  for  an  hour  at  105°  and  the  residue  can  usually  be  com- 
pletely extracted  in  three  hours  if  the  apparatus  used  is  efficient, 
and  if  not  more  than  3  gm.  of  sample  is  used.  Time  can  be  saved 
and  greater  accuracy  assured  if  the  extraction  is  continued  for  an 
hour,  the  almost  completely  extracted  residue  ground  very  fine 
and  the  extraction  continued  for  an  hour  longer. 

II.   OUTLINE  OF  THE  METHOD  OF  PROCEDURE 

Preparation  of  the  Sample.  Select  eight  or  ten  nuts  of  aver- 
age size  and  maturity  and  remove  the  husks  and  the  brown  skin 
which  envelops  the  seeds  by  means  of  a  thin-bladed  knife.  Place 
the  seeds  on  a  porcelain  plate  or  watch  glass  and  cut  into  thin 
slices  with  a  knife,  then  place  in  an  agate  mortar  and  crush  to  a 
pulpy  mass  till  free  from  lumps.  Weigh  out*3  gm.  of  the  sample 
into  a  closed,  dry  weighing  bottle,  place  in  a  drying  oven  and  keep 
at  a  temperature  of  105°  for  an  hour.  Determine  the  loss  in 
weight  which  results  and  calculate  the  percentage  of  water  present. 

The  Extraction.  Transfer  the  dried  sample  to  a  paper  or 
alundum  extraction  shell  and  cover  with  a  half-inch  layer  of  cotton 
wool,  which  has  been  previously  extracted  with  ether  to  remove 
the  small  amount  of  fat  which  it  usually  contains.  Place  the  shell 
in  an  extraction  tube  similar  to  B  of  Fig.  40  or  to  Fig.  42.  Weigh 
accurately  a  clean,  dry  fat-flask  of  1J25  cc.  capacity,  add  35  cc.  of 
pure  dry  ethyl  ether  and  connect  with  the  extraction  tube  by  means 


DETERMINATION   OF  CRUDE  FAT  IN  PEANUTS        213 

of  an  accurately-fitting  cork  stopper.  Connect  the  extraction 
tube  with  the  vertical  condenser  as  shown  in  Fig.  45  and  adjust 
the  cork  stoppers  so  that  the  flask  rests  directly  on  one  of  the  iron 
heating  plates,  then  start  the  water  running  thru  the  condenser. 
Close  the  switch  which  operates  the  heating  device  and  after  the 
ether  begins  to  boil  reduce  the  rate  at  which  it  boils,  if  this  seems 
to  be  necessary,  by  interposing  a  thin  sheet  of  asbestos  over  the 
heating  plate.  Adjust  the  end  of  the  condenser  so  that  all  of  the 
condensed  ether  falls  inside  the  extraction  shell  and  allow  the 
process  of  extraction  to  continue  for  three  hours. 

Weighing  the  Crude  Fat.  Disconnect  the  extraction  tube 
and  flask  from  the  condenser,  remove  to  some  distance  from  any 
source  of  heat  and  allow  to  drain  for  about  five  minutes.  Dis- 
connect the  flask  from  the  extraction  tube  and  then  connect  the 
flask  with  one  of  the  branches  of  the  block-tin  condenser  tube. 
Place  a  receiving  flask  under  the  other  end  of  the  tin  condenser 
tube  and  allow  the  ether  to  distil  over  until  only  about  2  cc.  of 
yellow  or  brown  oil  remains.  Then  remove  the  flask  and  place  in 
a  water-jacketed  oven,  heat  the  water  to  boiling  and  keep  at  this 
temperature  for  an  hour.  Draw  a  current  of  dry  air  thru  the 
flask  by  means  of  an  aspirator  until  the  residue  gives  no  odor  of 
ether.  Allow  the  flask  to  cool  and  weigh  accurately.  Calculate 
the  percentage  of  crude  fat  in  the  dried  sample  and  in  the  original 
selected  nuts. 


CHAPTER  XXXI 

ANALYSIS   OF  BLACK  POWDER 
I.   FACTS  UPON  WHICH  THE  ANALYSIS  Is  BASED 

Composition.  "  Black  powder  "  designates  a  mixture  of  char- 
coal, sulfur  and  either  sodium  or  potassium  nitrate;  it  is  largely 
used  as  an  explosive,  especially  for  blasting.  Such  mixtures  are 
easily  resolved  into  their  essential  constituents  by  first  leaching 
out  the  soluble  salts  with  water,  then  extracting  the  sulfur  by 
means  of  carbon  disulfide  and  assuming  that  the  residual  solid 
is  charcoal.  Altho  the  different  ingredients,  are  ground  very  fine, 
and  intimately  incorporated  in  the  mixture,  the  solvents  named 
readily  act  upon  it  since  the  charcoal  makes  the  mixture  porous, 
and  there  are  no  cell  membranes  thru  which  the  solvents  must  pass 
to  bring  the  soluble  constituents  into  solution. 

II.   OUTLINE  OF  THE  METHOD  OF  ANALYSIS* 

Determination  of  Moisture.  Weigh  out  2  gm.  of  the  sample 
.  on  a  3-inch  watch  glass,  spread  out  as  a  thin  layer  and  dehydrate, 
either  by  allowing  to  remain  in  a  desiccator  which  contains  con- 
centrated sulfuric  acid,  for  a  period  of  three  days,  or  by  heating 
in  an  oven  at  70°  for  several  hours  or  until  the  weight  remains 
constant.  The  temperature  must  be  kept  low  to  avoid  any 
possibility  of  volatilizing  some  of  the  sulfur.  Calculate  the  per- 
centage of  water  lost. 

Determination  of  Nitrates.  Weigh  out  10  gm  of  the  crushed 
sample  into  a  Gooch  crucible,  which  is  designed  to  be  used  in  a 

*  Bull.  51  of  the  U.  S.  Bureau  of  Mines  by  Walter  O.  Snelling  and  C.  G. 
Storm. 

214 


ANALYSIS  OF  BLACK  POWDER  215 

Wiley  extraction  apparatus  (see  Fig.  41),  weigh  accurately  and 
connect  with  a  suction  flask  in  the  usual  manner.  Wash  with  at 
least  200  cc.  of  warm  water  added  in  quantities  of  about  10  cc.  at 
a  time,  and  test  the  last  washings  for  nitrates  by  removing  a  few 
drops  and  adding  at  least  an  equal  volume  of  strong  sulfuric  acid 
in  which  a  few  crystals  of  diphenylamine  have  been  dissolved. 
This  test  will  yield  a  deep  blue  color  if  even  traces  of  nitrates  are 
present.  When  all  the  nitrates  have  been  leached  out,  remove 
the  crucible,  dry  at  70°  until  the  weight  is  constant  and  calculate 
the  percentage  of  nitrates  present  from  the  difference  between  the 
total  loss  in  weight  and  that  due  to  the  moisture  originally  present 
in  the  sample. 

Determination  of  Sulfur.  Place  the  crucible  containing  the 
residue  from  the  last  determination  in  a  Wiley  extraction  appara- 
tus and  extract  with  about  35  cc.  of  recently  distilled  carbon  disul- 
fide  for  about  one  hour.  Remove  the  crucible,  allow  most  of  the 
carbon  disulfide  to  evaporate  spontaneously,  dry  to  constant 
weight  at  70°  and  calculate-  the  percentage  loss  as  sulfur. 

Determination  of  Charcoal  and  Ash.  Calculate  the  percent- 
age of  charcoal  from  the  weight  of  residue  left  in  the  crucible. 
Burn  off  the  organic  matter  in  the  crucible,  weigh  the  residual  ash 
and  calculate  the  percentage  present. 


SECTION  V 
PARTITION  PROCESSES 


CHAPTER  XXXII 

GENERAL  FEATURES   OF  PARTITION  PROCESSES 

Consulate  Liquids.  When  two  liquids,  which  do  not  react 
with  each  other  chemically,  are  mixed  one  or  more  liquid  phases, 
depending  on  the  specific  properties  of  the  two  liquids,  may 
result.  With  certain  pairs  of  liquids  an  infinite  number  of  homo- 
geneous solutions  representing  every  possible  ratio  of  the  two 
constituents  can  be  prepared;  this  is  true  of  the  liquids,  alcohol 
and  water.  With  other  pairs  of  liquids  the  possibilities  are 
limited;  either  liquid  may  become  saturated  with  respect  to  the 
other,  and  if  a  greater  amount  of  one  liquid  than  is  required  to 
saturate  the  other  is  added,  a  new  liquid  phase  separates.  One 
of  the  resulting  liquid  phases  usually  contains  a  relatively  large 
amount  of  the  first  liquid  but  is  saturated  with  the  second;  the 
other  usually  contains  a  relatively  large  percentage  of  the  second 
liquid  but  is  saturated  with  the  first.  If  small  amounts  of  water 
are  successively  added  to  ether,  and  the  mixture  is  shaken  after 
each  addition,  a  single  phase  containing  a  relatively  large  amount  of 
ether  is  first  obtained,  but  when  the  amount  of  water  added  exceeds 
3  per  cent  by  volume  of  the  ether  used,  a  second  phase  containing 
about  90  per  cent  of  water  separates.  The  addition  of  further 
quantities  of  water  does  not  change  the  composition  of  either 
phase,  but  increases  the  amount  of  the  water-rich  phase  at  the 
expense  of  the  ether-rich  phase,  and  if  a  sufficient  amount  is  added 

216 


GENERAL  FEATURES  OF  PARTITION  PROCESSES       217' 

will  cause  the  entire  disappearance  of  the  latter.  The  addition 
of  still  further  quantities  of  water  merely  increases  the  percentage 
of  water  in  the  water-rich  phase. 

Many  pairs  of  liquids,  such  as  kerosene  and  water,  are  so  slightly 
soluble  in  each  other  that  the  addition  of  a  very  small  amount  of 
one  liquid  to  the  other  at  once  produces  two  distinct  phases,  whose 
composition  is  practically  the  same  as  that  of  the  pure  solvents. 
Any  pair  of  liquids  which  exist  as  independent  phases  after  being 
shaken  together  and  allowed  to  stand  until  equilibrium  has  been 
attained  are  spoken  of  as  "consolute"  liquids.  The  mutual 
solubility  of  two  consolute  liquids  is  affected  very  greatly  by  tem- 
perature changes.  Increasing  the  temperature  usually  increases 
their  mutual  solubility  and  may  cause  them  to  become  soluble  in 
any  proportions  whatever,  that  is,  may  result  in  the  disappearance 
of  one  of  the  two  phases. 

The  Distribution  Coefficient.  When  a  small  amount  of  a  third 
substance  is  added  to  a  system  consisting  of  two  consolute  liquids, 
the  whole  shaken  for  some  time,  and  allowed  to  stand  until  per- 
fect equilibrium  has  resulted,  the  added  substance,  or  a  certain 
part  of  it,  distributes  itself  between  the  two  phases.  The  ratio  of 
the  concentration  of  the  dissolved  substance  in  one  phase  to  the 
concentration  in  the  other  is  a  definite  quantity,  which  is  inde- 
pendent of  the  magnitude  of  the  concentrations  concerned,  pro- 
vided the  dissolved  substance  does  not  dissociate  and  does  not 
form  molecular  aggregates.  This  ratio  can  be  easily  determined 
experimentally  and  is  known  as  the  " distribution  coefficient." 
Its  value  is  affected  to  some  extent  by  temperature  changes.  If 
the  two  liquids  are  but  slightly  soluble  in  each  other,  and  if  the 
added  substance  is  much  more  soluble  in  one  than  in  the  other  the 
value  of  the  distribution  coefficient  will  be  either  very  large  or  very 
small,  depending  upon  which  of  the  two  solutions  concerned  is 
taken  as  the  standard  of  comparison.  If,  however,  the  two  liquids 
possess  a  more  nearly  equivalent  solvent  power  for  the  added 
substance,  or  if  the  two  liquids  dissolve  one  another  to  a  large 


218 


QUANTITATIVE  CHEMICAL  ANALYSIS 


extent,  so  that  the  composition  of  the  two  resulting  liquid  phases 
does  not  greatly  differ,  the  value  of  the  distribution  coefficient 
becomes  more  nearly  equal  to  unity. 

The  Separation  of  Consolute  Liquids.  The  two 
liquid  phases  which  make  up  a  consolute  mixture 
can  be  mechanically  separated  by  a  variety  of  de- 
vices. The  simplest  method  is  to  insert  a  pipet  or 
a  tube,  similar  to  the  one  shown  in  Fig.  46,  into 
the  mixture  till  its  end  is  slightly  above  the  plane 
separating  the  two  layers,  to  draw  the  upper  layer 
into  the  tube  by  suction,  and  transfer  the  liquid 
to  another  vessel.  The  separation  thus  effected 

46  is  always  imperfect  as  it  is  impossible  to  remove  all  of 

Separately  the  upper  layer  without  also  removing  some  of  the 
Pipet  lower  layer,  but  this  error  is  comparatively  small  if 

the  area  of  the  containing  vessel  at  the  point  of  contact  of  the 
two  layers  is  small. 

A  much  more  satisfactory  device  is  a  "separatory 
funnel,"  one  of  the  many  forms  of  which  is  represented 
in  Fig.  47.  This  is  provided  with  a  glass  stopper  and 
a  side  tube,  which  can  be  closed  with  the  finger  or  a  good 
cork,  so  that  the  two  consolute  liquids  can  be  shaken 
together  vigorously.  The  lower  of  the  two  resulting 
layers  can  then  be  allowed  to  drain  into  another  vessel 
by  opening  the  glass  stopcock  at  the  bottom  of  the 
funnel.  The  inaccuracy  of  the  separations  made  with 
such  a  device  is  due  almost  wholly  to  the  small  volume 
of  the  heavier  liquid  which  adheres  to  the  inner  surface 
of  the  tube  below  the  stopcock;  for  this  reason  this  tube 
should  be  made  as  short  as  possible  and  of  such  a  pig.  47.— 
diameter  that  capillarity  does  not  prevent  it  from  Separatory 
discharging  readily  after  the  stopcock  has  been  closed. 

Difficulties  arise  in  the  separation  of  two  consolute  liquids  when 
one  or  both  liquids  show  a  tendency  to  " emulsify,"  that  is,  to 


GENERAL  FEATURES  OF  PARTITION  PROCESSES       219 

form  an  intimate  mixture  composed  of  small  bubbles  of  the  two 
liquids,  which  do  not  segregate  except  after  very  long  standing. 
Instances  occasionally  arise  in  which  this  difficulty  is  sufficient 
to  make  the  process  concerned  an  impracticable  one.  The  pres- 
ence of  any  finely  divided  solid  matter  always  retards  and  may 
prevent  an  entirely  satisfactory  segregation  of  the  two  liquids. 

General  Theory  of  Partition  Processes.  Iodine  is  much  more 
soluble  in  the  liquid  carbon  tetrachloride  than  in  water  and  these 
two  liquids  are  but  slightly  soluble  in  each  other.  As  a  consequence 
of  these  facts  the  distribution  coefficient  of  iodine  between  the 
consolute  liquids  which  result  when  carbon  tetrachloride  is  added 
to  an  aqueous  solution  of  iodine,  has  at  ordinary  temperatures  the 
value  85.  This  means  that  every  unit  volume  of  the  carbon  tetra- 
chloride-rich  phase  will  contain  eighty-five  times  as  much  iodine 
as  each  unit  volume  of  the  water-rich  phase.  The  total  amount 
of  iodine  separated  from  an  aqueous  solution  by  this  treatment 
would  also  depend  on  the  volume  of  the  aqueous,  as  compared 
with  that  of  the  carbon  tetrachloride  phase.  Suppose,  for  example, 
it  is  assumed  that  the  aqueous  solution  has  a  volume  of  100  cc.  and 
contained  0.2  gm.  of  iodine,  that  50  cc.  of  carbon  tetrachloride  is 
added,  and  that  the  changes  in  volume  which  result  after  equilib- 
rium has  been  established  are  insignificant.  If  x  represents  the 
weight  of  iodine  in  the  resulting  aqueous  phase  0.2  -  x  must 
represent  the  weight  of  iodine  in  the  carbon  tetrachloride  phase. 
The  distribution  coefficient  would  require  that 

x      0.2  -  x     1  .  Q- 

ioo:~^o~ 

When  this  expression  is  solved  for  x  the  latter  is  found  to  have  the 
value  0.0046,  that  is,  the  weight  of  iodine  in  the  aqueous  solution 
is  reduced  to  4.6  mg.  by  this  treatment. 

If  now  the  carbon  tetrachloride  solution  is  separated  from  the 
mixture,  and  the  residual  aqueous  solution  is  again  treated  with 
50  cc.  of  carbon  tetrachloride  a  further  quantity  of  iodine  will  be 


220  QUANTITATIVE  CHEMICAL  ANALYSIS 

taken  up  by  the  latter.  If  y  represents  the  weight  of  iodine  left 
in  the  aqueous  solution  after  this  second  treatment,  the  distribu- 
tion coefficient  would  require  that 

y    .0.0046  -y. 
TOO*      ~^0~ 

The  value  of  y  calculated  from  the  expression  is  found  to  be 
0.0001016. 

The  calculation  shows  then  that  practically  all  of  the  iodine 
can  be  separated  from  the  aqueous  solution  by  two  treatments  with 
50  cc.  portions  of  carbon  tetrachloride.  It  can  be  readily  shown 
that  the  use  of  only  75  cc.  of  this  liquid  in  three  25  cc.  portions 
would  have  left  only  0.018  mg.  of  iodine  in  the  aqueous  solution 
and  in  general,  several  treatments  with  small  amounts  of  carbon 
tetrachloride  is  more  efficient  and  economical  than  fewer  treat- 
ments with  larger  amounts.  It  is  also  obvious  that  the  smaller 
the  volume  of  the  solution  from  which  the  substance  is  to  be 
determined  is  separated,  the  greater  the  efficiency  of  the  process. 

In  general,  the  theory  of  partition  processes  shows  a  close 
analogy  to  that  already  developed  in  discussing  the  washing  of 
precipitates,  but  unlike  the  latter  it  does  not  involve  the  use  of 
assumptions  which  are  never  actually  realized.  Further  emphasis 
should  be  laid,  however,  on  the  qualification  already  noted,  namely, 
that  the  value  of  the  distribution  coefficient  may  change  with 
varying  concentration.  This  may  result  from  the  effect  of  varying 
concentration  upon  the  degree  of  ionization  or  of  hydration,  or 
upon  the  nature  of  the  substances  actually  present  in  the  solution 
concerned. 


CHAPTER  XXXIII 

DETERMINATION   OF  NICKEL  IN  NICKEL  STEEL 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Composition  of  the  Sample.  Alloys  of  nickel  and  iron,  which 
contain  from  1  to  14  per  cent  of  nickel  are  frequently  used  for 
structural  purposes  where  extreme  hardness  and  toughness  are 
demanded,  and  where  the  importance  of  these  factors  warrants  the 
extra  cost  of  such  an  alloy.  They  usually  contain  small  amounts, 
up  to  1  per  cent,  of  combined  carbon,  very  small  amounts  of 
silicon,  sulfur  and  phosphorus  and  sometimes  appreciable  amounts 
of  manganese  and  copper. 

Altho  nickel  hydroxide  is  readily  soluble  in  an  excess  of  am- 
monium hydroxide  this  reagent  cannot  be  used  to  effect  a  quantita- 
tive separation  of  nickel  from  iron,  unless  the  process  is  repeated 
several  times,  or  unless  the  percentage  of  iron  present  is  very 
small,  owing  to  the  occlusion  of  nickel  by  ferric  hydroxide.  The 
partition  process  devised  by  J.  W.  Rothe  is  an  extremely  con- 
venient and  rapid  method  for  making  this  separation. 

Theory  of  the  Separation.  Anhydrous  ferric  chloride,  unlike 
the  chlorides  of  aluminum,  nickel,  cobalt,  chromium,  manganese, 
zinc  and  copper,  is  readily  soluble  in  ethyl  ether.  If,  however, 
ether  is  added  to  an  aqueous  solution  of  ferric  chloride  very  little 
iron  is  taken  up  by  the  resulting  ethereal  solution  unless  a  large 
concentration  of  hydrochloric  acid  or  some  soluble  chloride  is  also 
present.  It  is  probable  that  only  unionized  ferric  chloride  is 
appreciably  soluble- in  ether,  and  that  the  element  cannot  be 
separated  by  the  use  of  ether  unless  the  ionization  of  the  ferric 
chloride  is  repressed  by  the  addition  of  hydrochloric  acid.  The 

221 


222  QUANTITATIVE  CHEMICAL  ANALYSIS 

best  results  are  obtained  when  the  iron  solution  treated  contains 
from  20  to  25  per  cent  of  this  acid. 

The  value  of  the  distribution  coefficient  which  is  concerned 
here  is  not  constant  but  varies  with  the  temperature  and  the 
concentration  of  both  acid  and  ferric  chloride  in  the  aqueous 
solution;  under  favorable  conditions  it  may  attain  a  value  of  100. 
The  values  for  the  distribution  coefficients  of  the  chlorides  of  the 
metals  named  above,  except  possibly  copper,  are  represented  by 
extremely  small  fractions. 

Conditions  Necessary  for  the  Separation.  The  rate  at  which 
iron  was  removed  from  an  aqueous  solution,  which  had  a  volume 
of  20  cc.  and  contained  in  addition  to  20  per  cent  of  hydrochloric 
acid  0.2054  gm.  of  iron  as  ferric  sulfate,  by  successive  treatments 
with  25  cc.  portions  of  ether,  is  shown  in  the  following  results. 

Iron  removed  by  first  treatment 0 . 1964  gm. 

Iron  removed  by  second  treatment 0.0075  gm. 

Iron  removed  by  third  treatment 0 . 0016  gm. 

Iron  removed  by  fourth  treatment 0.0007  gm. 

Iron  removed  by  fifth  treatment 0 . 0002  gm. 

Since  ferrous  salts  are  not  appreciably  soluble  in  ether  all  of  the 
iron  must  be  kept  in  the  ferric  condition  during  the  separation. 
As  ether  reduces  ferric  salts  appreciably  at  a  temperature  slightly 
above  the  normal  the  mixture  must  be  kept  cold.  It  is  further 
necessary  to  keep  the  concentration  of  all  anions  except  chlorine 
low;  if  such  anions  are  present  they  may  keep  some  of  the  iron  in 
such  a  form  that  it  is  not  easily  taken  up  by  the  ether. 

Determination  of  the  Separated  Iron.  Most  of  the  ether 
present  in  the  ethereal  solution  can  be  recovered  for  subsequent 
separations  by  distilling  in  a  suitable  apparatus;  were  it  not  so 
the  cost  of  the  method  would  often  be  prohibitive.  The  last 
traces  can  be  driven  off  by  evaporating  in  an  open  vessel;  the  iron 
which  has  been  reduced  during  the  distillation  and  evaporation 
must  be  oxidized  before  it  is  precipitated. 


DETERMINATION  OF  NICKEL  IN  NICKEL  STEEL       223 

Determination  of  the  Separated  Nickel.  The  decomposition 
voltage  of  the  nickel  ion  is  about  0.22  volt  higher  than  that  of  the 
hydrogen  ion.  It  can  be  rapidly  and  completely  separated  in  a 
dense  form  from  a  neutral  solution  of  the  double  oxalate,  or  from 
solutions  of  the  sulfate  to  which  a  large  excess  of  ammonium 
hydroxide  has  been  added.  In  the  presence  of  the  N03  ion  a  small 
amount  of  nickel  oxide,  which  is  not  easily  redissolved,  may  sepa- 
rate at  the  anode.  The  precipitated  metal  is  not  dissolved  appre- 
ciably by  the  ammoniacal  solution  and  it  is  not  easily  oxidized. 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Preparation  of  the  Solution.  Weigh  out  2  gm.  of  the  sample, 
which  should  be  in  the  form  of  drillings  or  shavings,  into  a  300  cc. 
beaker,  add  20  cc.  of  dilute  hydrochloric  acid,  5  of  dilute  nitric 
acid,  cover  with  a  watch  glass  and  warm  the  mixture  until  the  alloy 
is  dissolved.  Remove  the  watch-glass  cover  and  evaporate  the 
solution  cautiously  to  avoid  loss  from  spattering  until  a  thick  syrupy 
liquid  or  solid  residue  remains.  Add  10  cc.  of  concentrated  hydro- 
chloric acid  to  the  residue  and  evaporate  as  before;  finally  dissolve 
the  residue  in  10  cc.  of  dilute  hydrochloric  acid,  dilute  to  20  cc., 
filter  off  the  small  residue  of  silica  and  carbon  on  a  7  cm.  filter  and 
wash  free  from  soluble  salts,  using  the  smallest  necessary  amount 
of  cold  wash  water. 

Separation  of  the  Iron.  Concentrate  the  filtrate  to  a  volume 
of  10  cc.,  allow  to  cool  and  then  transfer  the  solution  to  a  100  cc. 
separatory  funnel  with  the  aid  of  10  cc.  of  dilute  hydrochloric 
acid  and  50  cc.  of  ether.  Place  both  glass  and  cork  stoppers  in 
the  funnel,  cool  the  latter  under  a  stream  of  water  from  the  tap, 
shake  cautiously  once  and  release  the  excess  of  pressure  created 
in  the  funnel  by  cautiously  opening  the  cork  stopper.  Replace  the 
cork  stopper,  again  cool  the  funnel  and  shake  vigorously  for  about 
three  minutes.  Support  the  funnel  in  a  vertical  position  by  means 
of  a  clamp  and  allow  it  to  stand  until  the  plane  separating  the 
two  consolute  liquids  is  clearly  defined.  Remove  the  cork  stopper 


224  QUANTITATIVE  CHEMICAL  ANALYSIS 

and  cause  the  aqueous  phase  to  drain  into  the  beaker  previously 
used,  allowing  sufficient  time  to  permit  the  aqueous  phase  to  flow 
down  the  inner  surface  of  the  funnel  and  several  drops  of  the 
ethereal  phase  to  flow  through  the  stopcock;  then  rinse  off  the 
lower  end  of  the  funnel  with  2  or  3  cc.  of  water.  These  precau- 
tions become  necessary  for  the  purpose  of  rinsing  every  drop  of 
the  aqueous  phase  out  of  the  funnel  before  attempting  to  remove 
the  ethereal  phase.  Allow  the  ethereal  phase  to  flow  into  a  200  cc. 
Erlenmeyer  flask,  rinse  off  the  inner  and  outer  surfaces  of  the  tube 
below  the  stopcock  with  3  to  5  cc.  of  water,  then  close  the  stop- 
cock and  set  the  flask  aside.  Transfer  the  aqueous  solution  in  the 
beaker  to  the  funnel  with  the  aid  of  25  cc.  of  ether  and  again  mix 
and  separate  the  ethereal  layer.  Connect  the  Erlenmeyer  flask 
containing  the  combined  ether  extracts  with  a  condenser  and 
carefully  distil  off  the  ether,  which  can  be  used  for  subsequent 
determinations.  t 

Separation  of  Last  Traces  of  Iron.  Add  cautiously  5  cc.  of 
concentrated  sulphuric  acid  to  the  aqueous  solution  and  warm 
gently  until  the  ether  present  is  expelled,  then  heat  nearly  to  the 
boiling  point  and  evaporate  the  solution  until  fumes  of  sulphur 
trioxide  appear;  next  add  50  cc.  of  water,  and  digest  until  soluble 
salts  are  dissolved,  then  add  5  cc.  of  hydrogen  peroxide  to  oxidize 
any  iron  which  may  have  been  reduced  by  the  ether,  heat  to  the 
boiling  point  and  add  an  excess  of  ammonium4 hydroxide,  that 
is,  sufficient  to  impart  a  strong  odor  to  the  solution.  Keep  the 
solution  at  or  near  the  boiling  point  for  a  few  minutes,  then  filter 
off  the  precipitated  iron  and  manganese  on  a  7  cm.  filter  and  wash 
with  the  smallest  necessary  amount  of  hot  water. 

Determination  of  Nickel.  Ignite  and  weigh  accurately  a  clean 
platinum  electrode,  preferably  of  gauze.  Place  the  electrode  and 
a  platinum  spiral  in  the  nickel  solution,  add  20  cc.  of  dilute  am- 
monium hydroxide  and  make  the  proper  connections  with  the 
terminals  of  a  storage  battery.  If  a  gauze  electrode  has  been 
prepared  use  a  current  of  one  ampere  and  allow  the  action  to  con- 


DETERMINATION  OF  NICKEL  IN  NICKEL  STEEL       225 

tinue  for  at  least  fifteen  minutes  after  the  solution  has  become 
colorless.  If  a  foil  electrode  has  been  prepared,  it  will  be  prefera- 
ble to  use  a  current  of  one  half  ampere  only.  Remove  the  cathode, 
wash  in  alcohol,  dry  at  100°  and  weigh.  Calculate  the  percentage 
of  nickel  present.  Remove  the  nickel  from  the  cathode  by  allow- 
ing it  to  stand  in  a  cylinder  of  strong  nitric  acid  for  twenty 
minutes  and  rinse  off  the  acid  with  water. 

III.   QUESTIONS  AND  PROBLEMS.    SERIES  14 

• 

1.  Calculate  the  values  of  the  distribution  coefficient  for  iron  in  the  ethereal 
as  compared  with  the  aqueous  phase  at  different  concentrations  from  the  data 
given  on  page  #,/$  , 

2.  Discuss  the  factors  to  which  tlie  changes  in  the  values  of  this  distribu- 
tion coefficient  are  due. 

3.  Write  out  a  probable  reaction  for  the  reduction  of  ferric  chloride  by 
ether. 

4.  Suggest  a  probable  effect  of  the  presence  of  alcohol  in  the  ether  used  for 
this  separation. 

6.  What  objections  are  there  to  precipitating  the  iron  by  means  of  ammo- 
.  nium  hydroxide  without  previous  oxidation? 


CHAPTER  XXXIV 

DETERMINATION   OF   CAFFEINE  IN   TEA 
I.   FACTS  UPON  WHICH  THE  DETERMINATION  Is  BASED 

Properties  of  Caffeine.  The  stimulating  properties  of  tea  and 
coffee  are  due  for  the  most  part  to  caffeine.  This  compound  is  rep- 
resented by  the  formula  C8Hi0N402,  but  it  crystallizes  with  one 
molecule  of  water,  which  it  begins  to  lose  when  heated  to  110°. 
It  belongs  to  that  class  of  organic  compounds  which,  owing  to  their 
weakly  basic  properties,  are  known  as  alkaloids.  It  begins  to  be 
appreciably  volatile  at  100°,  melts  at  225°,  and  can  be  sublimed 
without  decomposition.  It  is  soluble  in  about  seventy-four  parts 
of  water,  eight  of  chloroform  and  2270  of  ether.  The  salts  which 
it  forms  with  acids  are  more  soluble  in  water  than  the  free  base. 

Properties  of  Chloroform.  One  volume  of  chloroform  requires 
nearly  183  volumes  of  water  to  dissolve  it  and  the  composition 
and  properties  of  the  consolute  liquids  formed  when  chloroform 
and  water  are  mixed  are  essentially  those  of  the  pure  compo- 
nents. Pure  chloroform  has  a  specific  gravity  of  1.526,  it  boils 
at  61°  and  its  vapor  is  not  inflammable;  although  it  is  an  expen- 
sive reagent  it  is  easily  recovered  and  purified  after  use. 

When  caffeine  is  in  equilibrium  with  chloroform  and  water  the 
concentration  in  the  chloroform  layer  is  about  thirteen  times  as 
great  as  in  the  aqueous  layer.  Although  this  ratio  is  not  very 
large  it  is  so  much  larger  than  the  ratio  representing  the  distribu- 
tion of  inorganic  salts  between  chloroform  and  water  that  caffeine 
can  be  easily  separated  from  these  salts  by  a  partition  process. 

Composition  of  Tea  Leaves.  Tea  contains  in  addition  to 
from  1  to  5  per  cent  of  caffeine,  soluble  inorganic  salts,  tannic  acid, 

226 


DETERMINATION  OF  CAFFEINE  IN  TEA  227 

coloring  matter  and  small  amounts  of  essential  oils  and  organic 
acids.  If  the  leaves  are  extracted  with  a  sufficient  amount  of  hot 
water  all  of  the  caffeine  and  most  of  the  tannin,  inorganic  salts 
and  organic  acids  are  brought  into  solution.  If  the  aqueous  solu- 
tion is  treated  with  a  sufficient  amount  of  a  solution  of  basic  lead 
acetate  the  tannin  and  organic  acids  form  insoluble  lead  salts,  but 
the  caffeine  remains  unprecipitated.  The  excess  of  lead  acetate 
necessarily  added  can  be  separated  by  passing  hydrogen  sulfide 
through  the  solution,  and  the  excess  of  hydrogen  sulfide  used  can  . 
be  boiled  off. 

Sources  of  Error.  The  small  amount  of  caffeine  present  in 
tea  makes  it  desirable  to  use  several  grams  of  the  sample  for  the 
determination.  The  residue  which  remains  after  the  extraction 
occupies  a  large  volume  and  is  difficult  to  filter  and  wash  thor- 
oughly. The  precipitate  of  lead  salts  is  also  very  bulky  and  forms 
a  dense,  impervious  coating  on  the  filter,  which  is  difficult  to  wash. 
These  errors  are  made  as  small  as  possible  by  weighing  out  about 
5  gm.  of  the  sample  and,  after  digesting  with  water  and  separating 
the  impurities,  diluting  to  500  cc.,  allowing  the  insoluble  residue 
to  settle  and  removing  an  aliquot  part  of  the  clear  solution.  This 
procedure  involves  a  positive  error  since  it  is  assumed  in  the  sub- 
sequent calculations  that  the  total  volume  of  the  solution  was 
500  cc.  Altho  a  rough  estimate  of  the  volume  occupied  by  the 
solid  matter  could  be  made  and  a  correction  introduced  the  proc- 
ess involves  other  negative  errors,  and  a  better  result  is  obtained 
if  the  error  is  disregarded.  Even  where  the  greatest  care  is  ex- 
ercised the  percentage  error  of  the  method  is  comparatively  large. 

II.   OUTLINE  OF  METHOD  OF  PROCEDURE 

Preparation  of  Aqueous  Solution.  Prepare  the  sample  by 
crushing  the  leaves  in  an  agate  mortar  till  fine  enough  to  pass 
thru  a  forty-mesh  sieve.  Weigh  out*  5  gm.  of  the  sample,  transfer 
to  a  500  cc.  graduated  flask,  add  400  cc.  of  water,  heat  slowly  to 
the  boiling  point,  taking  care  to  prevent  the  mixture  from  boiling 


228  QUANTITATIVE  CHEMICAL  ANALYSIS 

over,  and  keep  slightly  below  this  temperature  for  a  half  hour. 
Cool  the  mixture  to  the  temperature  of  the  room  and  add  slowly 
and  with  constant  agitation  4  cc.  of  a  solution  of  basic  acetate  of 
lead;  *  this  should  be  sufficient  to  precipitate  all  of  the  tannin  and 
coloring  matters  present.  Dilute  the  mixture  to  exactly  500  cc., 
mix  thoroughly  and  allow  to  stand  until  the  solid  matter  present 
settles. 

Remove  by  means  of  a  pipet  20  cc.  of  the  clear  solution  and 
allow  it  to  pass  thru  all  cm.  filter  into  a  clean  200  cc.  graduated 
flask  but  discard  the  filtrate  thus  obtained  since  the  paper  may 
have  absorbed  an  appreciable  amount  of  caffeine.  Remove  and 
filter  further  quantities  of  the  solution  until  the  flask  is  filled  to  the 
200  cc.  mark.  Transfer  the  200  cc.  of  filtrate  to  a  400  cc.  beaker 
and  pass  hydrogen  sulfide  thru  the  solution  until  the  precipitated 
lead  sulfide  becomes  granular.  Filter  into  another  400  cc.  beaker, 
wash  with  a  small  amount  of  cold  water,  evaporate  the  solution  to 
100  cc.  and  allow  to  cool. 

Separation  of  Caffeine.  While  waiting  for  the  solution  to 
evaporate,  clean  a  100  cc.  Erlenmeyer  flask  dry  in  an  air  bath, 
allow  it  to  cool  in  the  balance  room  for  at  least  half  an  hour  and 
weigh  accurately,  using  a  glass  counterpoise  of  about  the  same 
surface  area. 

Transfer  the  aqueous  solution  to  a  200  cc.  separatory  funnel, 
add  20  cc.  of  chloroform,  place  both  stoppers  in  the  funnel  and 
shake  vigorously  for  three  minutes.  Support  the  funnel  in  a 
vertical  position  by  means  of  a  clamp,  remove  the  cork  stopper, 
place  the  previously  weighed  flask  under  the  funnel  and  by  care- 
fully manipulating  the  stopcock  allow  the  chloroform  solution  to 
drain  into  it  until  the  plane  dividing  the  two  liquids  barely  reaches 
the  stopcock.  Rinse  off  the  lower  end  of  the  funnel  with  a  few 
drops  of  pure  chloroform  added  from  a  pipet  and  receive  the 

*  Prepared  by  boiling  430  gm.  normal  lead  acetate,  130  gm.  litharge  and 
1000  cc.  water  for  an  hour,  allowing  to  cool  and  settle,  and  diluting  until  the 
specific  gravity  is  1.25. 


DETERMINATION  OF  CAFFEINE  IN  TEA  229 

rinsings  in  the  flask.  Repeat  the  treatment  with  two  more  20  cc. 
portions  of  chloroform. 

Weigh  accurately  1  or  2  inches  of  fine  platinum  wire  and  add  to 
the  flask.  Connect  the  flask  with  a  condenser  by  means  of  a 
glass  tube  and  cork  stoppers,  start  the  water  running  through  the 
condenser  and  cautiously  distil  off  the  chloroform  until  only  a  few 
drops  of  solution  remain  but  avoid  heating  the  flask  much  above 
the  boiling  point.  The  platinum  wire  should  reduce  the  tendency 
of  the  solution  to  boil  over  materially.  Return  the  distillate 
obtained  to  the  stock  bottle  for  future  determinations. 

Again  extract  the  aqueous  solution  with  three  20  cc.  portions 
of  chloroform,  receiving  the  chloroform  solution  in  the  Erlenmeyer 
flask  previously  used  and  again  distil  off  the  chloroform. 

Disconnect  the  flask  from  the  condenser  while  still  warm, 
introduce  a  glass  tube,  which  is  attached  to  an  aspirator  or  water 
pump,  to  within  a  half  inch  of  the  bottom  of  the  flask  and  draw 
air  thru  it  for  several  minutes.  Place  the  flask  in  an  air  bath 
heated  to  75°  for  a  half  hour,  <again  draw  air  thru  it,  allow  to  cool 
and  weigh.  The  separated  caffeine  should  consist  of  fine  needle- 
like  crystals  of  a  nearly  white  color.  Calculate  the  percentage 
present. 

III.   QUESTIONS  AND  PROBLEMS.     SERIES  15 

1.  Calculate  the  weight  of  caffeine  which  should  be  removed  by  each  suc- 
cessive treatment  of  the  pure  aqueous  solution,  assuming  that  the  weights  and 
volumes  used  correspond  exactly  to  those  called  for  in  the  method  outlined. 

2.  Calculate,  as  in  the  previous  problem,  the  weights  of  caffeine  which 
should  be  removed,  assuming  however  that  1  cc.  of  the  chloroform  solution 
is  left  with  the  mixture  after  each  treatment. 

3.  What  compounds  would  you  expect  to  find  in  the  aqueous  solution  finally 
left  from  the  determination  of  caffeine  in  tea? 

4.  What  methods  could  you  use  to  test  the  purity  of  the  caffeine  finally 
separated  from  the  tea? 

5.  Is  it  at  all  probable  that  any  of  the  caffeine  would  remain  in  the  aqueous 
solution  as  a  salt  of  hydrogen  sulfide? 


SECTION  VI 
GENERAL  FEATURES  OF  VOLUMETRIC  PROCESSES 


CHAPTER  XXXV 

THEORY    OF  VOLUMETRIC   PROCESSES 

Fundamental  Definitions.  Volumetric  analysis  is  that  branch 
of  quantitative  analysis  in  which  the  amount  of  an  element  or 
compound,  which  is  present  in  the  substance  submitted  to  analysis, 
is  calculated  from  the  volume  of  some  reagent  of  known  strength 
that  is  found  to  be  necessary  to  complete  a  reaction  with  the 
element  or  compound  being  determined.  A  reagent  especially 
prepared  for  making  such  a  determination  is  known  as  a  "  standard 
solution."  The  value  of  this  solution  may  be  expressed  either  in 
terms  of  the  number  of  grams  of  reagent  actually  present  in  a 
unit-volume,  or  in  terms  of  the  number  of  grams  of  any  substance 
with  which  the  reagent  in  one  unit-volume  reacts.  The  process 
of  determining  the  volume  of  standard  solution  necessary  to  com- 
plete a  reaction  with  a  solution  of  the  substance  which  is  being 
analyzed,  and  in  general  the  process  of  comparing  the  relative 
strengths  of  two  solutions  which  react  with  each  other  chemically, 
is  designated  as  "  titrating." 

The  essential  difference  between  gravimetric  and  volumetric 
processes  consists  in  the  substitution  of  a  measurement  of  a  stand- 
ard solution  for  a  determination  of  the  weight  of  a  precipitate, 
or  of  some  product,  which  is  separated  from  the  substance  being 
analyzed.  Since  volumetric  processes  necessarily  involve  calcu- 
lating the  magnitude  of  a  weight,  which  corresponds  to  the  weight 

230 


THEORY  OF  VOLUMETRIC  PROCESSES  231 

of  precipitate  or  other  product  separated  in  a  gravimetric  process, 
they  are  virtually  indirect  methods  of  carrying  out  gravimetric 
processes. 

Reactions  Suitable  for  Volumetric  Processes.  Volumetric 
processes  are  usually  based  upon  definite  chemical  reactions  but 
only  a  limited  number  of  reactions  can  be  employed  in  making 
volumetric  determinations.  In  general  only  those  reactions  which 
take  place  completely  and  instantaneously  when  equivalent 
amounts  of  the  reacting  substances  are  present  are  suitable  for 
volumetric  processes.  For  this  reason  reactions  which  result  in 
the  formation  of  new  phases,  or  which  give  rise  to  products  which 
are  but  slightly  ionized,  are  largely  used.  A  number  of  reactions 
which  are  sufficiently  complete  but  not  instantaneous  become 
so  upon  the  addition  of  a  slight  excess  of  the  reagent  used  for  the 
preparation  of  the  standard  solution.  Such  reactions  are  some- 
times used  as  the  basis  of  volumetric  processes  by  the  method  of 
"back  titration."  In  employing  this  device  a  slight  excess  of  the 
standard  solution  is  added,  and  the  excess  added  is  then  titrated 
with  a  second  standard  solution,  which  reacts  completely  and 
instantaneously  with  the  standard  solution  first  employed.  If  the 
volumetric  relation  between  the  two  standard  solutions  has  been 
previously  determined,  the  proper  correction  for  the  excess  of 
standard  solution  first  added  is  easily  made. 

Determination  of  the  End-point.  A  second  requirement, 
which  reduces  still  further  the  number  of  reactions  which  can  be 
used  for  volumetric  determinations,  is  that  some  method  can  be 
devised  to  determine  the  point  at  which  the  amount  of  standard 
solution  added  is  equivalent  to  the  substance  being  titrated.  As 
this  point  is  approached  certain  of  the  physical  and  chemical 
properties  of  the  solution  change  very  rapidly;  in  some  cases  there 
is  a  marked  change  in  the  color  or  electrical  conductivity  of  the 
mixture,  in  others  a  precipitate  may  begin  to  form  or  may  just 
cease  to  form,  in  still  others  the  addition  of  another  reagent,  that 
is,  an  "  indicator/7  causes  a  decided  color  change  to  take  place. 


232  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  point  at  which  a  sufficient  amount  of  the  standard  solution 
has  been  added  to  make  these  changes  recognizable  is  known  as 
the  " end-point"  of  the  titration.  The  difference  between  this 
point  and  the  point  at  which  an  equivalent  amount  of  the  standard 
solution  has  been  added,  that  is,  the  true  end-point,  must  be  small 
if  the  process  is  to  be  sufficiently  accurate. 

Theory  of  Indicators:  First  Case.  Whenever  an  indicator 
is  used,  the  physical  change  which  is  recognized  is  the  result  of 
a  chemical  reaction,  in  which  the  indicator  itself  is  one  of  the  active 
reagents.  The  indicator  may  react  either  with  the  substance 
being  determined  or  with  the  standard  solution  employed  in  making 
the  determination.  In  the  latter  case  the  reactions  concerned  may 
be  represented  by  the  following  equations,  in  which  X  represents 
the  substance  being  determined,  R  the  reagent  in  the  standard 
solution  being  used,  and  I  the  indicator  employed: 

(1)  X  +  I  +  R-+RX  +  I, 

(2)  I  +  R-+IR, 

(3)  IR  +  X-+RX  +  I. 

The  appearance  of  the  end-point  is  here  dependent  upon  the  con- 
centration of  IR  which  should  remain  equal  to  zero  as  long  as  an 
appreciable  concentration  of  X  is  present,  but  should  increase  in 
direct  proportion  to  the  amount  of  R  added  as  soon  as  the  con- 
centration of  X  has  been  reduced  to  zero.  In  other  words,  re- 
action (1)  must  be  completed  before  reaction  (2)  begins  to  take 
place,  but  reaction  (2)  must  take  place  promptly,  even  when  the 
concentrations  of  I  and  R  are  very  small. 

It  is  further  necessary  that  in  case  a  small  amount  of  the  com- 
pound IR  has  been  formed  during  the  earlier  part  of  the  titration, 
which  may  readily  result  from  imperfect  stirring  and  consequent 
accumulation  of  R  in  the  upper  layers  of  the  solution,  it  should 
react  with  X  according  to  equation  (3),  thus  preventing  the 
appearance  of  false  end-points.  Reaction  (3)  is  also  a  direct 


THEORY  OF  VOLUMETRIC  PROCESSES  233 

measure  of  the  preponderance  of  reaction  (1)  over  reaction  (2) 
in  the  presence  of  X,  that  is,  it  insures  the  completion  of  (1)  before 
(2)  begins  to  take  place. 

It  is  evident,  therefore,  that  the  closeness  of  the  agreement 
between  the  end-point  actually  recognized  and  the  true  end-point 
depends  upon  the  values  of  the  equilibrium  constants  of  the  three 
reactions  concerned. 

A  second  factor  which  is  of  some  importance  is  the  amount  of 
indicator  used.  In  those  cases  in  which  the  end-points  obtained 
depend  upon  a  change  from  one  specific  color  to  another  the  two 
colors  often  tend  to  mask  one  another  and  give  rise  to  a  series  of 
indeterminate  transition  tints.  It  is  then  desirable  that  the  entire 
amount  of  indicator  present  should  be  completely  transformed 
into  the  compound  possessing  the  different  color  by  the  slightest 
possible  excess  of  the  titrating  solution;  in  such  cases  only  a  small 
amount  of  indicator  may  be  used. 

If,  however,  the  solution  of  the  indicator  is  colorless,  and  the 
addition  of  an  excess  of  the  standard  solution  produces  a  specific 
color,  a  relatively  large  amount  of  indicator  may  sometimes  be 
used  to  advantage.  Increasing  the  concentration  of  the  indicator 
favors  the  completion  of  reaction  (2)  but  inhibits  reaction  (3). 
If,  therefore,  the  equilibrium  constant  for  (2)  is  somewhat  small 
and  that  of  (3)  is  sufficiently  large,  an  increase  in  the  amount  of 
indicator  used  should  increase  the  accuracy  of  the  process.  On 
the  other  hand  if  the  reaction  constant  for  (3)  is  too  small  and  that 
of  (2)  is  sufficiently  large,  a  decrease  in  the  amount  of  indicator 
used  should  increase  the  accuracy  of  the  process. 

Theory  of  Indicators  :  Second  Case.  If  the  indicator  used  re- 
acts with  the  substance  being  determined  the  series  of  reactions 
concerned  may  be  represented  as  follows: 


(4)  X  +  I-+IX 

(  5  )     X  +  IX  +  R  ->  RX  +  IX 

(6)  IX  +  R-+RX  +  I. 


234  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  appearance  of  the  end-point  is  here  dependent  upon  the 
concentration  of  I,  which  should  remain  equal  to  zero  as  long  as 
an  appreciable  concentration  of  the  excess  of  X  is  present.  The 
accuracy  of  the  process  is  determined  largely  by  the  magnitude 
of  the  three  equilibrium  constants  concerned. 

The  Advantages  of  Volumetric  Processes.  Volumetric  proc- 
esses carPusually  be  carried  out  much  more  rapidly  and  often 
demand  less  experience  and  skill  than  the  corresponding  gravi- 
metric processes.  The  time  needed  to  make  the  actual  titration 
is  usually  a  few  minutes  only  but  the  necessity  of  removing  inter- 
fering substances  and  of  transforming  the  substance  to  be  deter- 
mined into  the  most  suitable  form  often  increases  the  time  required 
for  the  entire  analysis  to  several  hours.  Many  are  more  accurate 
than  the  corresponding  gravimetric  processes  but  in  other  cases 
the  reverse  is  true.  They  avoid  the  errors  which  are  involved  in 
making  an  actual  separation,  that  is,  the  errors  resulting  from 
solubility,  from  occlusion  or  from  other  difficulties  which  yield  an 
impure  product,  and  from  actual  mechanical  losses.  On  the  other 
hand  they  necessarily  involve  certain  errors  in  the  preparation 
and  measurement  of  the  standard  solution  used  and  in  the  deter- 
mination of  the  end-point  of  the  reaction  upon  which  the  process 
depends. 

Principle  of  Compensating  Errors.  A  principle  which  can  be 
used  to  great  advantage  in  volumetric  processes  is  that  of  counter- 
acting the  errors  involved  in  the  actual  determination  by  equal 
errors  in  the  standardization  of  the  solution  used.  Assuming  that 
there  is  always  a  discrepancy  between  the  true  and  the  observed 
end-point,  it  will  generally  be  true  that  this  discrepancy  will  be 
constant  so  long  as  the  conditions  remain  constant.  If  the  solu- 
tion is  standardized  under  exactly  the  same  conditions  as  those 
which  must  obtain  in  the  actual  determination,  practically  all 
errors  are  eliminated  as  the  standard  solution  used  becomes  merely 
an  instrument  by  means  of  which  the  strengths  of  two  solutions 
of  the  same  substance,  one  representing  a  known  amount  of  a  pure 


THEORY  OF  VOLUMETRIC  PROCESSES  235 

compound  and  the  other  the  solution  of  unknown  concentration, 
are  compared.  Considered  from  this  point  of  view  it  is  preferable 
to  standardize  the  solution  by  comparing  with  a  known  weight 
of  the  substance  being  determined,  and  wherever  it  is  possible  to 
use  the  same  solution  for  the  determination  of  a  number  of  sub- 
stances, strict  accuracy  would  demand  that  the  solution  be  re- 
standardized  for  every  one  of  the  substances  for  which  it  is  to 
be  used. 


CHAPTER  XXXVI 


I 


MEASUREMENT   OF  THE   SOLUTIONS   USED   IN  VOLUMETRIC 
DETERMINATIONS 

I.   SOURCES  AND  METHODS  OF  AVOIDING  ERRORS 
Volumetric  Apparatus.     The  accuracy  of  volumetric  deter- 
minations depends  in  part  upon  the  accuracy  attained  in  the 
measurements  made  and  necessitates 
the    use  of   certain  special  forms  of 
apparatus. 

Burets  are  calibrated  glass  tubes  of 
uniform,  small  diameter,  designed  to 
measure  variable  amounts  of  liquids 
delivered  by  them,  when  supported 
in  a  vertical  position.  The  delivery 
of  the  liquid  which  is  being  measured 
is  controlled  in  the  form  first  used  by 
Geissler  (see  Fig.  49),  by  a  glass  stop- 
cock, and  in  the  form  first  used  by 
Mohr  (see  Fig.  48),  by  a  rubber  joint 
which  connects  the  end  of  the  tube  with 
a  glass  nozzle,  and  is  provided  with  a 
pinchcock  or  a  screw  clamp.  The 
former  have  the  disadvantage  of  re- 
quiring the  use  of  some  lubricant,  such 

as  a  mixture  of  beeswax  and  vaseline, 

' 


,.. 

.  Fig.  49—  Geiss- 

make  them  tight,  and  01  being  more       ler  Buret 


Fig.  48—  Mohr 
Buret 

expensive  and  more  easily  broken.    The 

latter  have  the  disadvantage  that  the  rubber  connection  is  acted 
wpon  to   some  extent  by  solutions  of   strong  alkalies  and  by 

236 


MEASUREMENT  IN   VOLUMETRIC  DETERMINATIONS     237 


certain  oxidizing  agents,  which  may  reduce  the  concentrations  of 
the  solutions  measured  in  them  appreciably. 

The  total  capacity  of  the  burets  usually  employed  is  either  100, 
50,  25  or  10  cc.;  the  50  cc.  buret  should  be  graduated  to  read 
tenths  of  a  cubic  centimeter  and  its  diameter  should  be  small 
enough  to  permit  of  estimating  fiftieths  of  a  cubic  centimeter 
with  reasonable  accuracy.  Burets  of  smaller  capacity  should  be 
made  of  tubes  having  a  still  smaller  diameter  in  order  to  make 
measurements  with  a  corresponding  degree'  of  accuracy.  Since 
two  readings  are  involved  in  each  measurement 
the  maximum  possible  error  in  the  use  of  a  50  cc. 
buret  should  not  exceed  one  twenty- 
fifth  of  a  cubic  centimeter  which 
corresponds  to  one-eighth  of  one  per 
cent  when  the  amount  measured  is  as 
much  as  50  cc. 

Pipets  are  tubes  of  much  smaller 
bore  than  burets,  designed  to  measure 
definite  amounts  of  liquid  only.  They 
are  usually  provided  with  an  enlarge- 
ment at  their  center,  as  in  Fig.  50, 
which  greatly  increases  their  capacity, 
and  a  single  mark  near  the  upper  end, 
which  indicates  the  point  to  which 
they  must  be  filled  to  deliver  the 
volume  for  which  they  are  calibrated. 
Sometimes  they  are  calibrated  by 
means  of  two  marks,  one  above  and  pig  51_Pipet 
Fig.  50— Pipet  tfae  other  beiow  tne  enlargement,  and 

in  this  case  the  value  of  the  pipet  is  determined  by  the  volume 
of  liquid  delivered  during  the  passage  of  the  meniscus  from  the 
upper  to  the  lower  mark.  The  so-called  measuring  pipets  (Fig.  51) 
lack  the  enlargement  at  the  center,  and  are  calibrated  like  burets; 
they  are  rarely  used  for  amounts  greater  than  10  cc.  The  form  o 


238  QUANTITATIVE  CHEMICAL   ANALYSIS 

the  pipet  should  be  such  as  to  permit  of  a  free  flow  of  the  liquid 
over  its  entire  inner  surface  when  held  vertically,  and  the  orifice 
should  be  small.  The  time  required  for  the  delivery  of  the  liquid 
from  a  50  cc.  pipet  should  not  be  less  than  20  seconds;  from  a  10  cc. 
pipet  it  should  not  be  less  than  10  seconds.  Where  properly  used 
the  error  involved  in  the  measurement  with  a  25  cc.  pipet  should 
not  exceed  one  one-hundredth  of  a  cubic  centimeter.  They  are  to 
be  preferred  to  burets  wherever  it  is  possible  to  use  them,  on 
account  of  the  greater  ease  and  accuracy  with 
which  they  may  be  manipulated. 

Graduated  flasks  (Fig.  52)  are  flat-bottomed, 
and  have  a  long  narrow  neck.  They  are  usually 
calibrated  to  contain  a  definite  volume,  but  may 
be  calibrated  to  deliver  that  volume.  The 
diameter  of  the  neck  should  be  small  as  compared 
with  its  capacity;  that  of  a  1000  cc.  flask  should 
not  exceed  20  mm.;  that  of  a  100  cc.  flask  should 
not  exceed  10  mm. 

The  uncertainty  involved  in  the  use  of  a  1000  cc. 
flask  should  not  exceed  a  tenth  of  a  cubic  centi- 
meter;   for  a  100  cc.  flask  it  should  not  exceed 
"  ^wo  one~hundredths  of  a  cubic  centimeter. 


ted  Flask 

Graduated  cylinders  are  cylindrical  glass  tubes 

provided  with  an  enlarged  base  or  foot  and  with  a  lip  for  pour- 
ing. They  are  calibrated  to  indicate  the  varying  amounts  of 
liquid  which  they  may  contain  and  are  employed  for  rough 
measurements  only. 

Error  from  Paralax.  Errors  may  result  from  inaccuracies  in 
reading  the  level  of  the  liquid  in  the  apparatus  used.  Unless  the 
liquid  being  measured  is  intensely  colored  the  lowest  point  on  the 
curve  of  the  meniscus  forms  the  most  satisfactory  point  of  refer- 
ence, with  which  to  compare  the  graduations  on  the  apparatus. 
Since  this  point  lies  at  the  center  of  the  tube  the  error  from  para- 
lax,  especially  where  the  tube  is  of  large  diameter,  must  be  avoided. 


MEASUREMENT  IN  VOLUMETRIC  DETERMINATIONS     239 


The  simplest  method  of  doing  this  is  to  hold  the  tube  so  that  its 
main  axis  is  perfectly  vertical,  and  make  all  measurements  with 
the  eye  held  at  such  a  level  that  the  line  of  sight  makes  an  angle 
of  90°  with  the  axis,  that  is,  the  measurement  is  made  from  the 
point  at  which  the  plane  tangent  to  the  meniscus  at  its  lowest 
point  and  perpendicular  to  the  axis  of  the  tube  cuts  the  wall  of  the 
apparatus. 

A  number  of  devices  may  be  employed  to  assist  in  maintaining 
the  eye  at  the  proper  position.  A  piece  of  looking  glass  may  be 
held  in  contact  with  the  back  of  the  tube 
and  the  level  of  the  eye  shifted  till  the  lowest 
point  of  the  meniscus,  the  graduation  nearest 
to  it,  and  the  reflection  of  that  graduation 
in  the  mirror  are  all  on  the  same  line,  as 
represented  in  Fig.  53.  A  piece  of  stiff 
paper  with  a  perfectly  straight  edge  may  be 
folded  around  the  tube  in  such  a  manner 
that  the  two  edges  of  the  paper,  the  one 
being  at  the  front,  the  other 

Fig.  53— Use  of  a  Mirror  at   the  back   of   the   tube, 
in  Reading  Buret         anc[  the  lowest  point  of  the 
meniscus  are  all  in  line  with  one  another. 

A  more  convenient  device  is  found  in  the 
Schellback  burets  (see  Fig.  54)  and  pipets  in  which 
a  strip  of  dark  blue  or  black  glass,  and  two  adjoin- 
ing strips  of  white  enamel  glass  are  introduced 
at  the  back  of  the  tube  directly  opposite  the 
graduations.  If  the  level  of  a  liquid  in  a  tube 
of  this  kind  be  observed  the  dark  strip  seems 
to  contract  to  a  point  just  opposite  the  meniscus, 
as  shown  in  the  sketch.  If  the  eye  is  held  at 
the  proper  level  this  becomes  an  exceedingly 


Fig.  54— Schell- 
back Buret 


i  lit?       U1UUC1       l^Vt/A       v*.*.*^       . 

.harp .point  of  reference  from  which  to  compare  the  gn 
on  the  tube. 


240  QUANTITATIVE  CHEMICAL  ANALYSIS 

Still  another  device  employed  with  burets  only  is  a  cylindrical 
glass  float  (Fig.  55)  provided  with  an  encircling  line  etched  on  its 
-  outer  surface.     By  comparing  the  projection  of  the 
l'  plane  of  this  circle  with  the  graduations  on  the 
tube  an  exceedingly  accurate  reading  can  be  made. 
Unless  the  float  is  properly  adapted  in  form   and 
size  to  the  bore  of  the  buret,  capillary  action  retards 
its  movement  as  the  level  of  the  liquid  changes,  and 
gives  rise  to  large  errors. 

If  the  liquid  being  measured  is  intensely  colored 
the  circle  formed  by  the  uppermost  points  on  the 
curve  of  the  meniscus  forms  the  most  satisfactory 
plane  of  reference  with  which  to  compare  the  gradua- 
tions  on  the  tube. 

Error  from  Drainage.  When  a  liquid  is  permitted 
Fig.  55—  Float  ^o  pass  ou^  of    a   buret   somewhat   rapidly   small 


amounts  adhere  to  its  inner  surface,  and  some  of 
it  gradually  flows  down  and  unites  with  the  liquid  still  remaining 
in  the  buret.  The  rapidity  with  which  the  level  of  the  liquid  in 
the  buret  attains  its  ultimate  position  depends  upon  the  viscosity 
of  the  solution,  the  area  and  form  of  the  surface  drained,  and  the 
rapidity  with  which  the  solution  has  been  permitted  to  flow  from 
the  tube.  The  viscosity  depends  in  turn  upon  the  chemical 
nature,  concentration  and  temperature  of  the  solution.  In  order 
to  avoid  errors  from  this  source  a  sufficient  interval  must  elapse 
between  the  time  at  which  the  flow  from  the  apparatus  is  stopped, 
and  the  time  at  which  the  reading  is  made.  The  minimum  value 
of  this  time  interval  is  easily  ascertained  by  a  series  of  simple 
experiments. 

In  the  use  of  pipets  both  the  drainage  from  the  inner  surface, 
and  the  capillary  action  at  the  nozzle  have  to  be  considered,  and  a 
definite  method  of  procedure  must  be  adopted,  both  in  calibrating 
the  pipet  and  in  its  subsequent  use.  The  conditions  which  yield 
the  most  uniform  results  are  obtained  when  the  nozzle  of  the  pipet 


MEASUREMENT  IN  VOLUMETRIC  DETERMINATIONS     241 

is  permitted  to  touch  the  wall  of  the  receiving  vessel  while  the 
liquid  is  flowing  from  it,  and  to  remain  in  contact  with  it  for  20 
seconds  after  the  main  part  of  the  liquid  has  been  delivered;  the 
attempt  to  blow  out  the  few  drops,  which  are  retained  by  the 
nozzle  as  the  result  of  capillary  action,  is  not  to  be  recommended. 

Error  from  Water  in  the  Apparatus.  It  is  usually  necessary 
to  rinse  measuring  apparatus  with  water  before  using  and  the 
amount  of  water  retained  by  the  apparatus  may  effect  an  appreci- 
able change  in  the  concentration  of  the  solution  measured.  The 
error  can  be  avoided  by  drying  the  apparatus  before  use,  but  a 
more  convenient  method  is  to  rinse  it  out  with  some  of  the  solution 
which  is  to  be  measured  and  discard  the  rinsings.  The  amount  of 
liquid  used  for  this  purpose  should  be  at  least  10  per  cent  of  the 
total  capacity  of  the  measuring  vessel,  and  should  be  made  to  flow 
over  the  entire  inner  surface  by  repeatedly  shaking  or  by  inverting 
the  apparatus. 

Error  from  Changes  in  Temperature.  A  change  in  tempera- 
ture affects  both  the  size  of  the  vessels  used  and  the  density  of  the 
liquid  measured.  The  first  effect  is  practically  constant  for  tem- 
peratures ranging  from  zero  to  100°.  For  glass  vessels  of  the 
usual  form  this  so-called  " coefficient  of  cubical  expansion"  has 
the  value  0.000025,  which  represents  the  increase  in  the  capacity 
of  the  vessel  for  an  increase  of  one  centigrade  degree. 

The  second  effect  is  not  constant  even  over  small  ranges  of 
temperature  and  varies  greatly  with  the  liquid  concerned;  it  is 
much  greater  than  the  effect  on  the  containing  vessel.  All  or- 
ganic liquids  show  a  large  expansion  as  compared  with  water. 
The  expansion  of  dilute  aqueous  solutions^  such  as  are  used  in 
most  volumetric  determinations,  does  not  differ  greatly  from  the 
expansion  of  pure  water. 

The  actual  error  which  results  from  the  use  of  a  piece  of  gradu- 
ated apparatus  at  a  temperature  which  differs  from  that  at  which 
it  has  been  calibrated  is  due  to  the  difference  between  the  effect 
on  the  liquid  and  the  effect  on  the  containing  vessel.  It  is  a 


242  QUANTITATIVE  CHEMICAL  ANALYSIS 

simple  task  to  calculate,  from  the  coefficient  of  cubical  expansion 
of  glass  and  from  a  table  showing  the  expansion  of  water  for  dif- 
ferent temperatures,  a  series  of  factors  which  represent  the  num- 
ber by  which  the  observed  volume  should  be  multiplied  to  correct 
for  departures  in  temperature  from  that  for  which  the  apparatus 
was  calibrated. 

Error  from  Variations  in  the  Unit  of  Volume  Employed.  The 
choice  of  a  unit  of  volume  is  determined  solely  by  convenience, 
but  it  is  essential  that  the  same  unit  be  employed  in  all  the  opera- 
tions involved  in  any  one  determination.  The  standard  liter, 
that  is,  the  volume  occupied  by  a  kilogram  of  water,  when  weighed 
in  a  vacuum  and  measured  at  a  temperature  of  4°  is  manifestly 
inconvenient.  The  so-called  "Mohr  unit"  which  is  the  volume 
of  a  kilogram  of  water  when  weighed  in  the  air  with  brass  weights 
at  a  temperature  of  17.5°  is  more  convenient,  since  these  condi- 
tions do  not  differ  greatly  from  those  normally  prevailing  in  the 
laboratory.  Other  units  involving  measurements  at  tempera- 
tures of  15°,  16°  or  20°  have  been  used  by  other  chemists.  The 
exact  value  of  any  of  these  units,  in  terms  of  absolute  metric  units, 
can  be  determined  by  calculating  the  changes  in  volume  which 
take  place  when  a  flask  containing  sufficient  water  to  counter- 
balance a  kilogram  brass  weight  at  4°  in  a  vacuum  is  heated  to  a 
temperature  corresponding  to  the  unit  of  volume  concerned,  and 
when  an  amount  of  water  sufficient  to  counterbalance  the  buoyant 
effect  of  the  air  which  results  from  allowing  air  at  atmospheric 
pressure  to  replace  the  vacuum,  is  added. 

Much  of  the  calibrated  apparatus  sold  by  manufacturers  bears 
no  mark  by  means  of  which  the  unit  volume  represented  can  be 
determined,  and  even  when  this  is  clearly  designated  the  percentage 
error  represented  may  be  large.  It  is  not  advisable,  therefore,  to 
use  any  piece  of  calibrated  apparatus,  when  the  work  in  hand 
demands  great  accuracy,  until  its  actual  value  has  been  determined. 

In  this  book  the  unit  of  volume  adopted  is  the  volume  occupied 
by  a  kilogram  of  pure  water  when  weighed  with  brass  weights  in 


MEASUREMENT  IN  VOLUMETRIC  DETERMINATIONS     243 

air  and  measured  either  at  15  or  20°.  The  factors  by  which  the 
volumes  found  at  temperatures  ranging  from  10  to  25°  must  be 
multiplied  in  order  to  obtain  the  true  volume  for  the  units  here 
adopted  are  given  in  the  following  table: 


Temperature  of 
actual  measure- 
ment 

Factor  for  appa- 
ratus calibrated  at 
15° 

Factor  for  appa- 
ratus calibrated  at 
20° 

10 

1.00047 

1.00124 

11 

1.00040 

1.00117 

12 

1.00032 

1.00109 

13 

1.00023 

1.00100 

14 

1.00012 

1.00089 

15 

1.0 

1.00077 

16 

0.99987 

1.00064 

17      " 

0.99972 

1.00049 

18 

0.99956 

1.00034 

19 

0.99940 

1.00018 

20 

0.99923 

1.0 

21 

0.99904 

0.99981 

22 

0.99884 

0.99961 

23 

0.99861 

0.99941 

24 

0.99841 

0.99919 

25 

0.99820 

0.99897 

DETAILED  DESCRIPTION  OF  METHOD  FOR  THE  CALI- 
BRATION OF  VOLUMETRIC  APPARATUS 

Cleaning  Graduated  Apparatus.  Carefully  clean  a  50  cc. 
buret  and  two  pipets,  preferably  of  10  and  25  cc.  capacity.  If 
their  inner  surfaces  are  contaminated  with  a  film  of  organic  matter, 
water  will  adhere  to  them  in  streaks  and  drops.  These  impurities 
should  be  removed  by  rinsing  either  with  a  strong  solution  of 
sodium  hydroxide  or  with  a  cleaning  mixture  made  by  saturating 
sulfuric  acid  of  1.6  specific  gravity  with  sodium  dichromate;  in 
extreme  cases  it  may  be  necessary  to  allow  the  apparatus  to  stand 
over  night  in  a  cylinder  filled  with  this  solution.  If  the  buret  is 
of  the  Mohr  type  the  rubber  connection  should  be  removed  since 


244  QUANTITATIVE  CHEMICAL  ANALYSIS 

it  is  injured  by  contact  with  this  solution.  This  connection  should 
be  pliable  and  not  too  long  and  the  glass  tip  should  have  a  fine, 
round  opening.  The  pinchcock  should  be  strong  enough  to  pre- 
vent leakage  even  when  the  buret  is  full  of  water. 

Reading  the  Buret.  Practice  reading  the  buret  partly  filled 
with  water  until  you  can  read  its  level  accurately  to  a  fiftieth  of  a 
cubic  centimeter  by  the  use  of  one  of  the  devices  described  on 
page  239.  Determine  the  minimum  length  of  time  which  must 
be  allowed  for  drainage  by  filling  with  water  to  the  zero  point  and 
allowing  the  water  to  flow  rapidly  from  the  delivery  tube  until 
its  level  reaches  one  of  the  lowest  graduations,  and  noting  the 
changes  in  level  at  intervals  of  one  minute  from  the  time  of 
closing  the  pinchcock. 

Calibration  of  the  Buret.  Weigh  accurately  to  0.01  gm.  a  dry 
35  cc.  weighing  bottle  or  a  small  beaker  with  a  watch-glass  cover. 
Fill  the  buret  with  distilled  water  whose  temperature  does  not 
differ  by  more  than  1°  from  either  15°  or  20°,  depending  upon 
whether  the  normal  temperature  of  the  laboratory  corresponds 
more  nearly  to  15°  or  20°.  Raise  the  delivery  tube  of  the  buret 
until  nearly  horizontal  and  while  still  holding  in  this  position  open 
the  pinchcock  until  the  air-bubble,  which  is  sometimes  present, 
has  been  driven  out,  then  lower  the  delivery  tube  and  again  open 
the  pinchcock  until  the  lowest  point  of  the  meniscus  corresponds 
exactly  with  the  zero  point  of  the  buret. 

Place  the  delivery  tube  of  the  buret  inside  the  weighing  bottle, 
open  the  pinchcock,  and  allow  5  cc.  of  water  to  pass  thru  it. 
Close  the  bottle  and  weigh  as  before,  then  read  and  record  the 
exact  position  of  the  water  in  the  buret.  Continue  to  remove  and 
weigh  5  cc.  portions  of  the  water  until  25  cc.  have  been  removed. 
Empty  the  water  from  the  bottle,  dry  and  again  weigh,  and  then 
calibrate  the  remaining  25  cc.  portion  of  the  buret. 

Prepare  a  table,  of  which  one  column  represents  the  weights  of 
water  delivered  between  the  zero  point  and  the  ten  other  points 
at  which  readings  were  made;  a  second  column,  the  corresponding 


MEASUREMENT  IN  VOLUMETRIC  DETERMINATIONS     245 


readings;  and  a  third  column,  the  figures  in  column^  two) diminished 
by  those  in  column  one.'  The  figures  in  the  third  column  repre- 
sent the  corrections  to  be  added  or  subtracted  from  the  apparent 
readings.  If  any  of  these  errors  amounts  to  as  much  as  0.05  cc. 
calibrate  the  buret  in  the  neighborhood  of  the  point  giving  this 
error  at  intervals  of  1  cc. 

Calibration  of  Pipets.  Weigh  to  0.01  gm.  a  clean  and  dry  > 
weighing  bottle  of  about  30  cc.  capacity.  Suck  up  pure  water 
whose  temperature  is  either  15°  or  20°  into  the  ^5  cc.  pipet  until 
the  level  of  the  liquid  is  above  the  mark  on  the  stem.  Close  the 
upper  end  of  the  pipet  with  your  finger,  which  should  be  perfectly 
dry,  and  then  by  gently  releasing  the  pressure  allow  water  to  flow 
out  until  the  lowest  point  on  the  curve  of  the  meniscus  corre- 
sponds to  the  mark  on  the  pipet.  Place  the  nozzle  of  the  pipet  in 
contact  with  the  inner  surface  of  the  weighing  bottle  and  allow 
the  water  to  flow  into  it  and  to  drain  for  20  seconds.  Close  the 
weighing  bottle  and  weigh  to  0.01  gm. 

Calibrate  the  10  e€ ."pipet  in  the  same  manner.  / 

Calibration  of  Flasks.  Clean  a  100  cc.  and  a  250  cc.  flask  and 
rinse  with  distilled  water.  Insert,  a  long  piece  of  glass  tubing 
which  is  attached  to  a  foot  bellows,  or  other  device  for  producing 
a  blast  of  air,  into  the  250  cc.  flask,  hold  the  latter  in  an  inclined 
position  with  the  neck  down  and  slowly  heat  the  body  of  the  flask 
by  means  of  a  smoky  flame  rotating  the  flask  about  its  axis  until 
drops  of  moisture  can  no  longer  be  recognized  in  the  interior  of 
the  flask.  Allow  it  to  cool,  clean  the  outside  surface,  and  weigh 
accurately. 

Fill  the  flask  with  water  at  the  standard  temperature  until  the 
lowest  point  on  the  meniscus  corresponds  to  the  mark  on  the  neck 
of  the  flask.  Place  on  a  balance  designed  to  carry  a  load  of  at 
least  500  gm.  and  weigh  to  0.01  gm.  Subtract  the  weight  of  the 
flask  from  the  weight  last  obtained  to  find  the  capacity  of  the 
flask. 

Calibrate  the  100  cc.  flask  in  a  similar  manner. 


246  QUANTITATIVE   CHEMICAL  ANALYSIS 

III.   QUESTIONS  AND  PROBLEMS.     SERIES  16 

1.  What  is  the  value,  in  terms  of  absolute  metric  units,  of  the  unit  of  volume 
here  adopted,  assuming  that  water  expands  from  1  to  1.000874  when  heated 
from  4°  to  15°,  and  that  the  coefficient  of  cubical  expansion  of  glass  is  0.000025 
per  degree;   also  that  the  flask  which  is  calibrated  weighs  150  gm.,  that  the 
specific  gravity  of  glass  is  2.5  and  that  of  the  brass  weights  used  is  8.3,  and 
that  1  liter  of  air  at  15°  weighs  1.2  gm.? 

2.  What  weight  of  water  would  you  use  if  you  desired  to  calibrate  a  liter 
flask  to  represent  an  absolute  metric  unit,  but  found  it  necessary  to  do  the 
work  at  a  temperature  of  15°  and  under  ordinary  atmospheric  conditions  ? 

v  3.  A  solution  which  has  been  standardized  at  a  temperature  of  15°  by  the 
use  of  a  buret  which  was  also  calibrated  for  this  temperature,  was  found  to 
contain  0.02  gm.  of  hydrochloric  acid  per  cc.;  if  some  of  this  solution  is  meas- 
ured out  of  the  same  buret  at  a  temperature  of  10°,  what  weight  of  hydrochloric 
acid  is  present  in  each  cc.  as  measured  out? 

>  4.  In  preparing  a  one-tenth  normal  solution  of  silver  nitrate  (which  should 
contain  0.010786  gm.  per  cc.)  5.7  gm.  of  pure  silver  was  weighed  out,  dissolved 
and  diluted  to  500  cc.  in  a  graduated  flask.  The  solution  in  this  flask  was 
emptied  into  a  bottle,  which  had  not  been  dried  and  which  contained  0.5  cc. 
of  water  adhering  to  its  sides,  and  further  0.4  cc.  of  the  silver  solution  was 
left  adhering  to  the  flask.  If  28.36  cc.  of  water  was  added  to  the  bottle  and 
the  mixture  shaken,  what  relation  would  the  resulting  mixture  bear  to  one- 
tenth  normal  strength? 

f  6.  The  volume  of  water  which  remains  adhering  to  a  500  cc.  flask  is  0.4  cc., 
how  large  a  volume  of  a  solution  which  is  to  be  measured  in  it  should  be  added 
to  the  flask  for  the  purpose  of  rinsing  it  out  so  that  the  concentration  of  the 
original  solution  shall  not  be  changed  by  more  than  one-hundredth  of  one 
per  cent? 


CHAPTER  XXXVII 

SYSTEMS  USED  IN  THE  PREPARATION  OF  STANDARD  SOLUTIONS 

The  Unitary  System.  The  general  expression  by  means  of 
which  the  result  of  a  volumetric  determination  is  calculated  is: 

Vol.  of  standard  solution 
"WtTtf  sample  used  =  PercentaSe  desired. 

The  use  of  this  expression  becomes  extremely  simple  if  /  repre- 
sents an  entire  integer  or  a  decimal  fraction  of  an  entire  integer. 
It  is  easy  to  prepare  standard  solutions  to  conform  to  this  require- 
ment. If,  for  example,  a  solution  of  sodium  chloride  is  being 
employed  for  the  determination  of  silver,  and  it  is  desired  to  make 
/  =  0.01,  each  cubic  centimeter  of  sodium  chloride  solution  must 
contain 

.  Mol.  Wt.  of  NaCl 

0.01  X      A,    w. — F-A >    or    0.00542  gm. 

At.  Wt.  of  Ag 

Even  when  the  process  concerned  is  a  complicated  one,  that  is, 
involves  the  use  of  a  series  of  reactions,  the  standard  solution  used 
for  the  final,  titrati on  can  be  made  to  conform  to  this  system,  which 
can  be  conveniently  designated  as  the  "unitary  system."  If, 
further,  the  weight  of  sample  used  for  the  analysis  is  exactly  one 
hundred  times  as  great  as  the  value  of  1  cc.,  every  cubic  centi- 
meter used  for  the  determination  represents  1  per  cent  of  the 
substance  being  determined,  and  the  percentage  present  corre- 
sponds to  the  number  of  cubic  centimeters  used  in  making  the: 
determination.  If,  for  instance,  1  gm.  of  alloy  is  weighed  out  for 
the  determination  of  silver  and  the  latter  is  determined  by  titrat- 
ing with  a  sodium  chloride  solution  containing  0.00542  gm.  per 

247 


248  QUANTITATIVE  CHEMICAL  ANALYSIS 

cubic  centimeter  the  percentage  of  silver  in  the  alloy  corresponds 
to  the  number  of  cubic  centimeters  used. 

So  long  as  standard  solutions  are  to  be  used  for  the  determina- 
tion of  only  one  substance  the  unitary  system  is  the  most  con- 
venient one  to  employ,  but  it  is  often  desirable  to  use  such  solution 
for  the  determination  of  a  variety  of  substances,  and  in  such  in- 
stances the  necessary  calculations  possess  the  desired  simplicity 
for  only  one  of  the  substances  concerned.  If,  for  example,  the 
solution  used  for  the  determination  of  silver  is  also  used  for  the 
determination  of  mercury  by  means  of  the  reaction  Hg2(NO3)2 
+  2  NaCl  —  >  Hg2Cl2  +  2  NaN03  the  value  of  /  becomes 


It  becomes  necessary  therefore,  when  this  system  is  used,  to  pre- 
pare a  separate  solution  for  every  substance  determined;  if  a  very 
large  number  of  determinations  of  these  substances  are  to  be  made 
this  may  be  a  desirable  thing  to  do,  but  frequently  the  extra  labor 
involved  in  preparing  and  using  the  several  different  solutions 
more  than  offsets  the  gain  in  making  the  calculations. 

General  Features  of  the  Normal  System.  When  the  standard 
solution  is  to  be  employed  only  occasionally,  and  for  the  determi- 
nation of  a  variety  of  substances,  it  is  preferable  to  make  use  of 
the  so-called  "  normal  system."  The  essential  idea  upon  which 
this  system  is  based  is  to  use  such  concentrations  that  equal  vol- 
umes contain  equivalent  amounts,  of  the  different  reagents  and 
therefore  that  a  mixture  composed  of  equal  volumes  of  any  two 
such  solutions  which  react  with  each  other  will  not  contain  an 
excess  of  either  reagent.  In  order  to  prepare  such  a  series  of  so- 
lutions it  is  necessary  that  the  standard  volume,  usually  the  liter, 
should  contain  amounts  of  the  active  reagents  which  bear  a  simple 
relation  to  the  molecular  weights  of  the  compound  concerned. 
The  exact  value  of  this  relation  may  be  conveniently  estimated 
by  comparing  the  chemical  activity  of  the  molecule  with  that  of 


THE  PREPARATION  OF  STANDARD  SOLUTIONS        249 

the  hydrogen  atom  as  a  unit  or  standard.  A  normal  solution  is 
then  denned  as  one  which  contains  in  a  liter  an  amount  of  the 
active  reagent  chemically  equivalent  to  1.008  gm.  of  hydrogen. 
Thus  a  normal  solution  of  any  acid,  which  contains  a  single  replace- 
able hydrogen  atom,  and  which  is  used  in  a  reaction  involving 
simple  neutralization,  must  contain  as  many  grams  of  that  acid  as 
there  are  units  in  its  molecular  weight.  A  normal  solution  of  any 
base  must  be  equivalent  to  a  normal  solution  of  any  acid;  and 
hence,  if  the  base  contains  a  single  hydroxyl  group,  the  liter  should 
contain  an  amount  corresponding  to  its  molecular  weight  expressed 
in  grams ;  if  it  contains  two  hydroxyl  groups  it  should  contain  one- 
half  as  many  grams  as  there  are  units  in  its  molecular  weight. 

Where  the  reagent  is  used  in  a  reaction  involving  oxidation,  or 
reduction,  or  precipitation,  exactly  the  same  principle  is  used.  In 
every  case  the  oxidizing,  or  reducing,  or  replacing  power  of  the 
molecule  concerned,  as  compared  with  the  oxidizing  or  reducing 
or  replacing  power  of  the  hydrogen  atom,  determines  the  number 
by  which  the  molecular  weight  must  be  divided  to  give  the 
normal  value.  This  number  will  be  designated  in  this  book  as 
the  "  activity/7  Further  details  as  to  the  method  of  computing  the 
normal  values  of  different  reagents  will  be  discussed  as  the  differ- 
ent processes  are  described. 

Normal  Values  Dependent  Upon  the  Reaction  Concerned. 
It  should  be  especially  noted  that  the  normal  value  of  a  substance 
may  vary  according  to  the  type  of  reaction  in  which  it  is  used. 
Thus  the  normal  value  of  a  solution  of  oxalic  acid  is  determined 
by  dividing  its  molecular  weight  by  two,  no  matter  whether  used 
as  a  neutralizing,  a  reducing,  or  a  precipitating  agent;  whereas 
the  normal  value  of  nitrous  acid  is  the  entire  molecular  weight, 
when  used  as  a  neutralizing  agent,  but  is  one-half  its  molecular 
weight  when  used  as  a  reducing  reagent.  Further  than  this  the 
same  reagent  may  be  used  in  two  reactions  which  belong  to  the 
same  type  and  have  a  different  normal  value  for  each.  Thus 
phosphoric  acid  may  be  used  in  reactions  in  which  it  acts  as  a 


250  QUANTITATIVE   CHEMICAL  ANALYSIS 

monovalent  or  a  divalent  acid;  in  the  former  case  its  normal  value 
is  the  entire  molecular  weight,  in  the  latter  case  it  is  one-half  its 
molecular  weight. 

Advantage  of  the  Normal  System.  Since  a  normal  solution 
of  any  reagent  must,  according  to  definition,  be  chemically  equiv- 
alent to  a  normal  solution  of  any  substance  with  which  it  reacts, 
every  cubic  centimeter  of  such  a  solution  must  be  equivalent  to 
as  many  grams  of  that  substance  as  are  present  in  a  cubic  centi- 
meter of  a  normal  solution  of  that  substance.  In  other  words  the 
value  of  1  cc.  of  a  standard  solution,  in  terms  of  any  substance 
with  which  it  reacts,  is  determined  by  dividing  the  molecular 
weight  of  the  substance  by  one  thousand  times  its  activity.  The 
general  expression  for  the  calculation  of  the  results  of  a  volumet- 
ric determination,  where  a  normal  solution  is  used  then  becomes: 

Vol.  of  solution  used       M  X  100 

Wt.  of  sample       X  IOOOX~I  =  per  cent  of  substance> 

where  M  is  the  molecular  weight  and  A  is  the  activity  of  the 
compound  determined. 

The  advantage  of  the  system  is  most  striking  where  the  process 
concerned  is  an  indirect  one,  that  is,  where  the  method  involves 
the  use  of  a  series  of  reactions.  In  such  cases  the  usual  stoichio- 
metric  method  requires  a  separate  calculation,  involving  one 
multiplication  and  division,  for  every  reaction  concerned.  By 
the  use  of  the  normal  system  it  is  possible  from  a  mere  inspection 
of  the  reactions  concerned,  to  calculate  the  value  of  the  solution 
being  used  in  terms  of  the  substance  being  determined,  by  a  single 
division.  For  example,  potassium  bitartrate  may  be  determined 
by  dissolving  in  water,  neutralizing  and  precipitating  as  calcium 
tartrate,  filtering  off  the  precipitate  and  converting  into  calcium 
carbonate  by  igniting  in  an  open  crucible  and  titrating  the  result- 
ing carbonate  with  standard  hydrochloric  acid.  The  reactions 
involved  are: 


THE   PREPARATION  OF   STANDARD  SOLUTIONS        251 

(1)  C4H5K06  +  KOH  ->  C4H4K206  +  H2O, 

(2)  C4H4K206  +  CaCl2  +  4  H20  ->  C4H4CaO64  H20  +  2  KC1, 

(3)  2  C4H4Ca064  H2O  +  5  02  ->  2  CaC03  +  6  C02  +  12  H20, 

(4)  CaC03  +  2  HC1  -» CaCl2  +  H20  +  C02. 

An  inspection  of  these  reactions  shows  that  each  molecule  of 
bitartrate  yields  one  of  neutral  tartrate,  one  molecule  of  neutral 
tartrate  yields  one  of  calcium  tartrate,  one  of  calcium  tartrate  yields 
one  of  calcium  carbonate  and  one  of  calcium  carbonate  is  equiv- 
alent to  two  of  hydrochloric  acid.  Since  the  hydrochloric  acid 
contains  one  replacable  hydrogen  atom  it  has  an  activity  of  one, 
hence  the  activity  of  the  calcium  carbonate  is  two  and  also  the 
activity  of  potassium  bitartrate,  when  determined  by  this  process, 
is  two.  The  formula  for  the  calculation  of  the  result  of  the 
determination  is: 

Wt.  of  sol.         mol.  wt.  of  C4H5K06 .  -  ~  „  Tjrrk 

X  ~        ov  innn         -  X 100  =  per  cent  of  C4H5K06. 


Wt.  of  sample  2  X  1000 

Use  of  Solutions  Which  Bear  a  Simple  Relation  to  Normal 
Strength.  Normal  solutions  are  too  concentrated  to  give  the 
best  results,  and  it  is  customary  to  prepare  solutions  which  bear 
a  simple  relation  to  normal  strength,  that  is,  are  either  one-half, 
one-fifth  or  one-tenth  normal.  The  results  obtained  by  the  use 
of  such  solutions  are  correctly  calculated  by  introducing  the 
factors  one-half,  one-fifth  or  one-tenth  in  the  formula  given  above. 

Even  where  the  solution  has  not  been  prepared  to  bear  a  simple 
relation  to  normal  strength  this  method  of  calculation  may  still  be 
employed  to  advantage.  The  relation  of  any  solution  to  normal 
strength  can  be  calculated  by  dividing  the  number  of  grams  of 
active  reagent  in  1  cc.  by  the  number  of  grams  present  in  1  cc.  of 
normal  solution  of  that  reagent;  or,  it  may  be  determined  by 
dividing  the  number  of  grams  of  any  substance  with  which  1  cc. 
reacts  by  the  number  of  grams  in  1  cc.  of  a  normal  solution  of  that 
substance.  The  resulting  factor  representing  the  exact  relation 
of  the  solution  to  normal  strength  is  then  used  in  the  above  formula 
just  as  the  simpler  factors  one-half,  etc. 


SECTION  VII 

VOLUMETRIC  PROCESSES   INVOLVING   PRECIPI- 
TATION 


CHAPTER  XXXVIII 

DETERMINATIONS  WHICH  DEPEND   UPON  THE  USE   OF   A 
STANDARD   SOLUTION   OF  SILVER  NITRATE 

I.  THEORY  UPON  WHICH  THE  METHODS  DEPEND 

Reactions  Between  Silver  and  Halogen  Ions.  The  reversi- 
bility of  the  reactions  which  take  place  between  solutions  contain- 
ing halogen  ions  and  silver  ions  depend  upon  the  solubility  of  the 
silver  halides  and  hence  is  very  small.  There  is  further,  in  dilute 
solutions  at  least,  no  tendency  for  the  formation  of  complex  ions 
or  the  separation  of  salts  of  abnormal  composition. 

Determination  of  End-Points  Without  an  Indicator.  When 
silver  chloride  first  separates  as  a  precipitate  it  is  finely  divided 
and  a  very  minute  quantity  of  it  can  be  recognized;  if  the  solution 
containing  it  is  shaken  vigorously  the  precipitate  coagulates,  leav- 
ing a  supernatant  liquid  which  is  perfectly  bright  and  clear.  Hence 
if  a  soluble  chloride  is  titrated  with  silver  nitrate  and  the  mixture 
well  shaken  in  a  stoppered  bottle  after  every  addition  of  silver 
solution,  the  point  at  which  the  addition  of  a  further  quantity  of 
solution  fails  to  produce  a  further  quantity  of  precipitate  can  be 
recognized.  Under  certain  conditions  this  method  of  determining 
the  end-point  admits  of  a  very  high  degree  of  accuracy  and  is 
widely  used  in  determining  the  fineness  of  silver  bullion.  As  it  is 
a  somewhat  tedious  method  and  demands  skill  and  experience  a 

252 


USE  OF  A  STANDARD   SOLUTION  OF  SILVER  NITRATE       253 

less  accurate  but  more  convenient  method,  which  depends  upon 
the  use  of  an  indicator,  is  usually  employed  when  the  less  valuable 
halogen  is  determined  by  the  use  of  this  reaction. 

Determination  of  End-Points  With  a  Chromate  Indicator. 
The  neutral  chromate  of  silver  has  an  intense  red  color,  and  altho 
its  solubility  is  small,  it  is  decidedly  greater  than  that  of  the  silver 
halides.  These  facts  suggest  the  possibility  of  using  a  solution 
of  a  neutral  chromate  as  an  indicator  in  the  titration  of  the  halo- 
gens with  a  silver  salt.  The  series  of  reactions  concerned  is 
represented  by 

(1)  Na  +  Cl  +  Ag  +  N03->  AgCl  +  Na  +  N~03, 

(2)  2  R  +  Cr64  +  2  Ag  +  2  N03  ->  Ag2Cr04  +  2  R  +  2  N~03, 

(3)  Ag2Cr04  +  2  Na  +  2  Cl  -»  2  AgCl  +  2  Na  +  Cr64. 

The  process  evidently  corresponds  to  the  first  of  the  two  general 
cases  discussed  in  Chapter  XXV.  The  value  of  the  equilibrium 

constant  of  (1)  is  1  -r-  (Ag)(Cl),  that  is,  corresponds  to  the  re- 
ciprocal of  the  solubility  product  of  silver  chloride  and  has  the 

value  1  -v-  (1.41  X  10~5)2,  or  0.5  X  1010.     The  value  of  the  equi- 

+ 
librium  constant  of  (2)  is  1  ^  (Ag)2  (Cr04),  that  is,  corresponds  to  the 

reciprocal  of  the  solubility  product  of  silver  chromate  and  has  the 
value  1  4-  1.71  X  10~12,  or  0.58  X  1012.  The  value  of  the  equilibrium 
constant  for  (3)  is  determined  by  the  ratio  of  (Cr04)  to  (Cl)2 
in  a  solution  which  is  saturated  with  both  silver  chloride  and 
silver  chromate.  This  ratio  can  be  calculated  as  follows: 

+      -  +          (1  41  X  10~5)4 

(Ag)(Cl)  =  (1.41X10-«)»,       or    (Ag)«=  - 


+  +          1  71  v  in-12 

(Ag)2(Cr04)  =  1.71  X  10-12,     or     (Ag)2  =    ' 


+ 

Since  both  equations  concern  the  same  solution  (Ag)  has  the 
same  value  for  both  equations  and  hence 


254  QUANTITATIVE  CHEMICAL  ANALYSIS 

(1.41XlO-5)4-i-(Cl)2  =  1.71  X  10-12  -*-(Cr64), 
or  (Cr64)  :  (Cl)2 :  :  1.71  X  lO"12  :  4  X  1Q-20, 

and  (Cr64)  :  (d)2 :  :  4.3    X  107 : 1. 

In  titrating  a  soluble  chloride  with  silver  nitrate  the  true  end- 
point  is  that  at  which  exactly  one  equivalent  of  silver  has  been 

+ 

added.     At  this  point  both  (Cl)  and  (Ag)  must  have  the  value 

1.41  X  10~5.  The  value  of  (Cr04),  which  must  be  present  in  order 
to  cause  Ag2Cr04  to  separate  as  soon  as  sufficient  silver  has  been 

added  to  reduce  (Cl)  to  1.41  X  10~5,  is  evidently  4.3  X  107  X 
(1.41  X  10-5)2,  or  0.86  X  1Q-2.  The  amount  of  soluble  chromate 

which  must  be  added  to  give  (CrO4)  this  value  is  large;  if  K2Cr04 

+ 
is  used  and  it  is  assumed  that  all  of  the  salt  is  dissociated  into  (K) 

and  (Cr04),  each  100  cc.  of  solution  would  have  to  contain  0.17  gm. 
This  concentration  is  sufficient  to  impart  a  deep  yellow  color  to  the 
solution  and  increases  to  some  extent  the  difficulty  of  recognizing 

small  amounts  of  Ag2CrQ4.  Reducing  (CrO4),  however,  produces 
a  much  smaller  reduction  in  the  corresponding  value  of  (Cl).  If, 
for  example,  (Cr04)  is  given  the  value  0.86  X  10~3  Cl  becomes 
0.45  X  10~5,  that  is,  reducing  (CrO4)  one-tenth  reduces  (Cl)  only 
one-third.  Furthermore,  the  total  volume  of  standard  solution 
needed  to  change  (Cl)  from  0.45  X  10~5  to  1.4  X  10~5  is  very 
small;  it  can  be  calculated  to  be  about  one  drop  of  a  one-tenth 
normal  solution  when  the  total  volume  of  the  solution  is  100  cc. 

It  should  also  be  noted  that  a  certain  minimum  amount  of 
Ag2Cr04  must  be  formed  before  it  can  be  recognized  with  cer- 
tainty. This  minimum  depends  upon  the  total  volume  of  the 
mixture,  the  amount. of  AgCl  and  the  extent  to  which  it  is  co- 
agulated, and  the  ability  of  the  analyst  to  recognize  slight  color 
changes. 


USE   OF  A    STANDARD   SOLUTION   OF  SILVER  NITRATE       255 

This  discussion  indicates  that  altho  a  relatively  large  amount 
of  indicator  should  be  used  in  the  titration,  moderately  large 
variations  in  this  amount  produce  a  comparatively  slight  effect 
upon  the  final  result.  It  is  also  evident  that  a  personal  factor  is 
involved  in  the  titration  and  it  is  desirable  to  eliminate  this  as  far 
as  possible  by  standardizing  the  silver  solution  with  a  known 
weight  of  a  pure  chloride  and  making  all  determinations  under 
exactly  the  same  conditions  as  were  adopted  in  the  standardization. 

Effect  of  Acids  Upon  the  Titration.  Altho  moderate  concen- 
trations of  even  largely  dissociated  acids  do  not  affect  "reaction 
(1)  appreciably  very  slight  concentrations  affect  reaction  (2)  to 
such  an  extent  as  to  make  it  impossible  to  determine  the  true  end- 
point  with  even  approximate  accuracy.  This  can  be  explained 
by  considering  the  reactions  which  take  place  when  silver  chro- 
mate  is  treated  with  nitric  acid,  namely, 

(4)  Ag2Cr04  +  H  +  NOs  ->  HCr04  +  2  Ag  +  N03, 

(5)  2  HCr04  ->  Cr~267  +  H20. 

Both  of  these  reactions  have  been  studied  quantitatively.*     The 

+       — 
equilibrium  constant  for  (4),  that  is,  (HCr04)  -f-  (H)  (CrO4)  has 

the  value  1.2  X  106  and  the  equilibrium  constant  for  (5),  that  is, 
(Cr2O7)  -f-  (HCr04)2  has  the  value  74.  The  combined  effect  of 
these  reactions  is  to  decrease  (CrO4)  by  an  amount  which  nearly 
equals  the  total  amount  of  hydrogen  ion  present.  As  the  solu- 
bility product  of  Ag2Cr207  has  the  value  2  X  10~7  there  is  but 
little  probability  that  this  salt  will  separate  unless  both  (H)  and 
(Ag)  in  addition  to  (CrO4)  are  large.  Still  another  effect  results 
from  the  fact  that  Cr2O7  ions  impart  a  red  instead  of  a  yellow  color 
to  the  solution  and  materially  increase  the  difficulty  of  recog- 
nizing small  amounts  of  Ag2CrO4. 

*  Sherrill,  Jour,  of  Am.  Chem.  Soc.,  29,  1641  (1907). 


256  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  presence  of  small  concentrations  of  hydroxyl  ions  is  not 
objectionable  provided  the  solubility  product  of  silver  hydroxide 
is  not  exceeded.  If  the  solution  is  made  neutral  toward  such  an 
indicator  as  litmus  or  rosolic  acid  no  difficulty  from  either  H  or  HO 
ions  will  be  experienced. 

Reactions  Between  a  Silver  Salt  and  a  Cyanide.  When  a 
silver  salt  is  first  added  to  a  solution  of  a  soluble  cyanide  a  com- 
plex ion  is  formed;  the  process  is  represented  by 

(6)  Ag  +  NOs  +  2R  +  2CN-+2R  +  Ag(CN)2  +  N03. 

The  value  of  the  equilibrium  constant  for  this  reaction,  that  is, 
Ag(CN)2  -T-  (Ag)  (CN)2  is  1  X  1021,  hence  the  amount  of  silver 
left  in  the  form  of  a  simple  ion  is  extraordinarily  small. 

As  the  solubility  product  of  KAg(CN)2  is  large  no  precipitate 
forms  nor  is  there  any  other  indication  of  the  progress  of  the  re- 
action. The  solubility  product  of  the  salt  AgAg(CN)2  has  the 
value  2.25  X  10~12  and  as  soon  as  sufficient  silver  has  been  added 
to  complete  reaction  (6)  a  slight  further  addition  brings  about  the 
reaction 

(7)  K  +  Ag(CN)2  +  Ag  +  N~03  -»  AgAg(CN)2  +  N03  +  K. 
Determination  of  End-Point  in  Titration  of  Cyanides.     When 

a  soluble  cyanide  is  titrated  with  a  silver  salt  the  point  at  which 
reaction  (6)  has  been  completed  and  (7)  begins  to  take  place  is 
shown  by  the  appearance  of  a  white  precipitate,  that  is,  AgAg(CN)2. 
Altho  the  solubility  product  of  this  salt  is  small  it  has  the  property 
of  coagulating  almost  at  once  and  small  amounts  of  it  are  not 
readily  recognized. 

Silver  iodide  is  less  soluble  and  more  difficult  to  coagulate  than 
silver  cyanide  and  when'  freshly  precipitated  an  extremely  small 
amount  of  it  can  be  easily  recognized.  If  a  solution  of  silver 
nitrate  is  added  to  a  solution  containing  both  cyanides  and  iodides 
silver  iodide  will  not  separate  as  long  as  (CN)  has  an  appreciable 
value,  since  the  equilibrium  constant  for  reaction  (6)  is  1  X  1021/ 


USE   OF  A   STANDARD   SOLUTION   OF   SILVER  NITRATE       257 

while  the  constant  for  the  reaction  representing  the  formation  of 
silver  iodide  is  the  reciprocal  of  its  solubility  product,  that  is, 

1  X  1016.     When  the  titration  has  been  carried  to  the  point  at  which 

+ 
(CN)  is  extremely  small  (Ag)  begins  to  increase  very  rapidly  and 

soon  attains  a  value  sufficient  to  cause  either  Agl  or  AgAg(CN)2 
to  separate.  As  the  solubility  product  of  Agl  is  1  X  10~16  and 
that  of  AgAg(CN)2  is  2.25  X  10~12  the  latter  precipitate  should 
not  separate  as  long  as  a  reasonably  large  concentration  of  soluble 
iodide  is  present.  Experience  shows  that  there  is  a  very  slight 
tendency  for  the  separation  of  some  silver  cyanide  with  the  iodide, 
but  this  tendency  is  entirely  suppressed  by  the  addition  of  a  small 
amount  of  ammonium  hydroxide.  This  is  one  of  the  most  easily 
recognized  and  accurately  defined  end-points  known. 

Method  of  Preparing  a  Standard  Silver  Solution.  Silver  which 
is  999.5  fine  can  be  obtained  from  dealers  and  an  accurately  stand- 
ardized solution  of  silver  nitrate  can  be  prepared  by  weighing  out 
the  proper  amount  of  metal,  dissolving  in  nitric  acid  without  loss 
and  diluting  accurately  to  the  calculated  volume.  If  the  solution 
is  to  be  used  with  the  chromate  indicator  the  excess  of  nitric  acid 
used  must  be  completely  expelled  or  accurately  neutralized.  Com- 
plete expulsion  cannot  be  assured  unless  the  solution  is  evaporated 
to  dryness  and  the  residual  salt  heated  to  about  198°,  that  is,  to 
the  fusion  point  of  the  salt.  As  silver  nitrate  begins  to  decom- 
pose slightly  above  this  temperature  it  must  be  heated  with  great 
care. 

II.   PREPARATION  AND  STANDARDIZATION  OF  A  ONE-TENTH 
NORMAL  SOLUTION  OF  SILVER  NITRATE 

Preparation  of  Solution.  Weigh  out  accurately  from  5.4  to 
5.8  gm.  of  pure  metallic  silver,  place  in  a  casserole  or  porcelain 
dish,  cover  with  a  watch  glass,  and  add  20  cc.  of  dilute  nitric  acid. 
If  action  does  not  begin  to  take  place  after  a  few  minutes,  or  if  it 
becomes  too  slow,  warm  gently  or  add  a  small  amount  of  strong 
acid.  When  the  metal  is  dissolved  rinse  off  the  under  side  of  the 


258  QUANTITATIVE   CHEMICAL  ANALYSIS 

watch  glass  and  set  it  aside,  then  place  on  the  steam  or  sand  bath 
and  evaporate  the  solution  to  complete  dryness.  If  the  sand  bath 
is  used  the  mixture  must  be  stirred  during  the  later  stages  of  the 
evaporation  to  avoid  losses  from  spattering.  Finally  raise  the 
temperature  to  the  point  at  which  the  nitrate  just  fuses,  noting 
that  since  the  solubility  curve  terminates  in  the  fusion  curve  and 
the  molten  nitrate  forms  a  nearly  colorless  liquid  this  transition 
may  escape  recognition.  The  complete  absence  of  white  fumes 
when  air  is  blown  over  the  hot  dish  is  sufficient  evidence  of  the 
complete  removal  of  nitric  acid. 

Allow  the  dish  to  cool,  dissolve  the  salt  in  a  little  water  and 
transfer  the  solution  to  a  500  cc.  graduated  flask,  using  the  rinsings 
of  the  dish  to  dilute  to  exactly  500  cc.  Place  a  cork  in  the  flask 
and  invert  several  times  or  until  the  mixture  is  homogeneous,  then 
transfer  to  a  clean  glass-stoppered  bottle,  which  has  been  allowed 
to  drain  for  about  five  minutes.  Calculate  the  volume  to  which 
the  silver  weighed  out  should  be  diluted  to  make  the  residual 
solution  exactly  one-tenth  normal,  that  is,  to  make  1  cc.  contain 
0.010788  gm.  of  silver,  and  add  to  the  bottle  from  a  buret  the 
necessary  amount  of  water,  then  shake  thoroughly.  Test  the 
solution  with  a  piece  of  blue  litmus  paper  for  acidity;  if  it  gives 
a  perceptible  reaction  it  must  be  neutralized  by  cautiously  adding 
very  dilute  sodium  hydroxide  and  the  small  amount  of  insoluble 
precipitate  formed  filtered  off. 

Standardization.  Weigh  out  from  0.23  to  0.28  gm.  of  pure 
recently  dried  sodium  chloride  into  a  200  cc.  Erlenmeyer  flask, 
add  35  cc.  of  water  and  one  of  a  5  per  cent  solution  of  pure  potas- 
sium chromate.  Rinse  out  a  clean  50  cc.  buret  with  10  cc.  of 
the  silver  solution  and  discard  the  rinsings,  then  fill  to  the  zero 
mark. 

Add  the  silver  solution  to  the  salt  solution  somewhat  rapidly 
until  the  red  precipitate  which  forms  temporarily  disappears 
slowly,  then  add  it  more  slowly  until  the  mixture  acquires  a  faint 
but  permanent  reddish  tinge.  If  shaken  vigorously  the  red 


USE   OF  A  STANDARD   SOLUTION  OF   SILVER  NITRATE       259 

chromate  of  silver  may  separate  with  the  silver  chloride  instead 
of  remaining  suspended. 

Calculate  the  weight  of  sodium  chloride  found  to  be  equivalent 
to  1  cc.  of  the  silver  solution  and  divide  by  the  weight  of  sodium 
chloride  in  1  cc.  of  a  normal  solution  of  sodium  chloride  to  obtain 
the  normality  factor. 

III.  DETERMINATION  OF  CHLORINE  IN  KAINITE 

Preliminary  Statements.  The  mineral  kainite  is  found  in  the 
Stassfort  salt  deposits,  and  is  one  of  the  important  sources  of 
potassium  salts.  It  is  sometimes  represented  by  the  formula 
KCl*MgS04'6  H20,  but  it  rarely  corresponds  exactly  with  this, 
and  furthermore  is  usually  associated  with  sodium  chloride  and 
other  salts.  Large  amounts  of  it  are  ground  and  used  directly  as 
a  fertilizer. 

The  Analysis.  Weigh  out  from  0.5  to  0.8  gm  of  the  sample 
into  a  260  cc.  Erlenmeyer  flask,  add4§0  cc.  of  water  and  titrate 
with  the  silver  solution  exactly  as  in  the  standardization.  Calcu- 
late and  report  the  percentage  of  chlorine  present;  by  making  ihe 
s  proper  substitutions  in  the  general  formula. 

IV.  DETERMINATION  OF  CHLORINE  IN  TAP  WATER 

Preliminary  Statements.  The  percentage  of  chlorine  in  well 
or  river  water  varies  greatly  and  its  determination  often  yields 
results  which  are  of  much  significance  in  deciding  whether  a  sample 
is  suitable  for  domestic  use,  for  irrigation  or  for  the  production 
of  steam.  Usually  the  amount  present  is  relatively  small  and  it 
is  desirable  to  measure  out  from  200  to  500  cc.  for  the  determina- 
tion. The  volume  of  silver  solution  required  to  produce  a  recog- 
nizable amount  of  silver  chromate  is  much  larger  than  in  the 
previous  titrations;  it  can  be  ascertained  by  determining  the 
volume  which  must  be  added  to  an  equal  volume  of  distilled  water, 
to  which  some  white  precipitate  such  as  zinc  oxide  or  calcium 


260  QUANTITATIVE  CHEMICAL  ANALYSIS 

carbonate  has  been  added,  to  yield  a  mixture  which  after  titration 
shows  the  same  color  change  as  the  sample.  The  white  precipi- 
tate is  added  to  produce  an  effect  similar  to  that  produced  by  the 
silver  chloride  in  the  sample. 

The  Analysis.  Test  the  sample  for  alkalinity  by  means  of  a 
piece  of  red  litmus  paper.  Measure  out  exactly  250  cc.  of  the 
sample  into  a  400  cc.  Erlenmeyer  flask  and  if  necessary  neutralize 
by  careful  addition  of  very  dilute  nitric  acid.  Next  add  1  cc.  of 
the  chromate  indicator  and  titrate  with  the  silver  solution  until 
a  recognizable  amount  of  silver  chromate  is  produced,  and  set  the 
flask  aside.  Measure  out  250  cc.  of  distilled  water,  add  0.2  gm. 
of  zinc  oxide  or  calcium  carbonate,  and  titrate  this  mixture  with 
the  silver  solution  until  it  shows  a  color  exactly  equal  to  that  of 
the  sample  in  the  flask  set  aside.  Subtract  the  volume  used  in 
titrating  the  distilled  water  from  that  used  in  titrating  the  sample 
and  calculate  the  weight  of  chlorine  ^corresponding  to  this  volume 
of  silver  solution.  Report  results  in  terms  of  grams  of  chlorine 
per  liter  of  water.  \s 

V.  DETERMINATION  OF  POTASSIUM  CYANIDE  IN  COM- 
MERCIAL "  CYANIDE" 

Preliminary  Statements.  The  commercial  "  cyanide  "  which 
is  so  largely  used  for  the  extraction  of  gold  and  silver  from  their 
ores  consists  of  a  mixture  of  sodium  and  potassium  cyanides 
together  with  small  amounts  of  carbonates,  chlorides,  ammonium 
salts  and  hygroscopic  water.  As  sodium  and  potassium  cyanide 
are  about  equally  efficient  solvents  for  the  treatment  of  gold  and 
silver  ores  it  is  customary  in  the  evaluation  of  such  cyanides  to 
determine  the  total  cyanogen  and  to  calculate  the  corresponding 
amount  of  potassium  cyanide.  As  the  cyanide  is  extremely 
hygroscopic  it  is  somewhat  difficult  to  secure  an  average  repre- 
sentative portion  of  a  large  sample,  unless  a  large  amount  is  taken 
for  the  analysis  dissolved  in  water  and  a  fractional  part  of  the 


USE   OF   A   STANDARD   SOLUTION  OF  SILVER  NITRATE       261 

solution  used  for  the  analysis.     Great  care  should  be  exercised  in 
handling  the  sample  as  it  is  extremely  poisonous. 

The  Analysis.  Crush  several  pounds  of  the  original  sample 
until  the  particles  do  not  exceed  grains  of  wheat  in  size,  place  at 
once  in  a  glass-stoppered  bottle  and  rotate  and  shake  the  latter 
until  thoroughly  mixed.  Add  about  5  gm.  of  the  sample  to  a 
weighing  bottle  and  weigh  accurately.  Transfer  the  salt  to  a 
250  cc.  graduated  flask,  dissolve  in  water,  dilute  to  exactly  250  cc. 
and  mix  thoroughly.  Remove  a  25  cc.  pipet  full  of  the  solution 
to  a  200  cc.  Erlenmeyer  flask,  being  very  careful  to  avoid  getting 
any  of  the  solution  into  the  mouth,  add  5  cc.  of  dilute  ammonium 
hydroxide,  then  2  cc.  of  a  5  per  cent  solution  of  potassium  iodidei/ 
and  finally  titrate  with  the  silver  solution  until  a  very  faint  but 
permanent  turbidity,  due  to  the  formation  of  silver  iodide,  appears. 
The  accuracy  of  the  determination  can  be  increased  by  holding 
the  flask  against  a  black  background  while  determining  the  end- 
point.  Calculate  the  percentage  of  potassium  cyanide  present 
from  the  volume  of  silver  solution  required,  noting  that  A  of  the 
general  formula  has  the  value  one-half. 

VI.  QUESTIONS  AND  PROBLEMS.    SERIES  17 

1.  What  volume  of  a  one-tenth  normal  solution  of  silver  nitrate  would  be 
required  to  saturate  100  cc.  of  a  solution  which  contained  0.3  gm.  of  potassium 
chromate  with  silver  chromate,  assuming  that  the  solubility  product  of  silver 
chromate  is  1.71  X  10~12? 

2.  If  a  standard  solution  of  silver  was  used  to  titrate  a  solution  containing 
bromine  ions,  what  concentration  of  potassium  chromate  should  be  present 
in  order  to  cause  silver  chromate  to  separate  as  soon  as  an  equivalent  amount 
of  silver  nitrate  had  been  added,  assuming  that  the  solubility  product  of  silver 
bromide  was  0.49  X  10~14?  ^ 

3.  If  solid  silver  nitrate  was  gradually  added  to  a  solution,  which^con-^^x 
tained  0.2  gm.  of  potassium  chromate  and  1.64  gm.  of  sodium  acetate^what 
weight  of  silver  nitrate  would  have  to  be  added  before  silver  acetate  would 
begin  to  separate,  assuming  that  the  solubility  product  of  silver  acetate  was 
3.48  X  10~3  and  that  all  the  salts  concerned  were  completely  dissociated? 


262  QUANTITATIVE  CHEMICAL  ANALYSIS 

4.  If  it  is  found  that  the  volume  of  silver  nitrate  solution  required  to  pro- 
duce a  recognizable  amount  of  silver  chromate  in  the  determination  of  kainite 
was  one  drop,  how  large  an  error  would  result  from  failure  to  correct  for  it? 

5.  If  the  results  obtained  for  the  determination  of  potassium  cyanide  in 
commercial  "cyanide"  exceeded  one  hundred  per  cent,  what  explanation 
might  be  suggested? 


CHAPTER  XXXIX 

DETERMINATION    OF   ZINC   BY   MEANS   OF  A   SOLUTION   OF 
POTASSIUM    FERRO CYANIDE 

.  I.   THEORY  UPON  WHICH  THE  METHOD  DEPENDS 

The  Reaction  Concerned.  When  a  dilute  solution  of  potas- 
sium ferrocyanide  is  slowly  added  to  a  solution  of  a  zinc  salt  a 
flocculent  precipitate  of  a  bluish  color  separates,  but  a  point 
is  finally  reached  at  which  the  precipitate  becomes  pulverulent 
and  pure  white.  The  precipitate  finally  obtained  contains  both 
potassium  and  zinc,  the  relative  amounts  of  which  may  vary 
according  to  the  conditions  under  which  the  precipitate  separates. 
It  is  not  known  whether  a  double  ferrocyanide  of  zinc  and  potas- 
sium is  formed  or  whether  potassium  ferrocyanide  is  adsorbed  by 
the  zinc  ferrocyanide  which  first  separates. 

In  devising  a  method  for  the  determination  of  zinc  based  upon 
this  reaction  it  is  necessary  to  adopt  certain  standard  conditions, 
and  a  preliminary  study  of  the  manner  in  which  varying  condi- 
tions affect  the  reaction  is  a  necessary  prerequisite  to  the  intelli- 
gent use  of  the  reaction.  Under  the  conditions  which  are  here 
adopted  the  reaction  is  represented  with  approximate  accuracy  by 

(1)        2  K4Fe(CN)6  +  3  ZnCl2  ->  K2Zn3[Fe(CN)6]2  +  6  KCL 

Determination  of  the  End-Point.  When  a  soluble  ferrocya- 
nide is  added  to  an  iron  salt  a  deep  blue,  or  when  added  to  a  salt 
of  copper,  cobalt  or  uranyl  a  deep  red-brown,  precipitate  sepa- 
rates. It  is  possible  to  recognize  a  smaller  amount  of  a  soluble 
ferrocyanide  by  means  of  a  uranyl  salt  than  of  the  other  salts 

263 


264  QUANTITATIVE  CHEMICAL  ANALYSIS 

mentioned  and  these  salts  form  the  best  indicators  for  this  titra- 
tion.  The  reaction  with  a  uranyl  salt  is  probably  represented  by 

(2)  2  (U02)  (C2H302)2  +  K4Fe(CN)6  -»  (U02)2Fe(CN)6 

+  4K(C2H302). 

The  equilibrium  constants  of  both  (1)  and  (2)  are  unknown,  but 
if  a  solution  of  potassium  ferrocyanide  is  added  to  a  solution  which 
contains  salts  of  both  zinc  and  uranyl  both  reactions  take  place, 
and  further,  if  a  solution  containing  zinc  and  potassium  chlorides 
is  added  to  a  solution  which  contains  suspended  uranyl  ferro- 
cyanide the  latter  is  not  affected.  This  indicates  that  the  equi- 
librium constant  of  the  reaction 

(3)  2  (U02)2Fe(CN)6  +  3  ZnCl2  +  2  KC1  ->  Zn3K2[Fe(CN)6]2 

+  4  (U02)C12 

has  a  comparatively  small  value  or  that  its  velocity  is  small.  On 
the  other  hand,  reaction  (3)  does  not  proceed  in  the  reverse  direc- 
tion, at  least  when  the  time  allowed  is  short,  and  a  solution  of  a 
uranyl  salt  can  be  used  to  test  a  solution  which  is  being  titrated, 
for  potassium  ferrocyanide,  since  the  addition  of  a  uranyl  salt 
will  not  produce  a  precipitate  of  uranyl  ferrocyanide  unless  an 
excess  of  potassium  ferrocyanide  is  present.  In  using  a  uranyl 
salt  as  an  indicator,  however,  it  is  necessary  to  remove  portions 
of  the  solution  from  time  to  time  during  the  progress  of  the 
titration  and  bring  it  into  contact  with  a  drop  of  the  indicator 
solution. 

Since  it  may  be  necessary  to  make  a  large  number  of  these  tests 
before  the  true  end-point  is  reached,  and  since  that  portion  which 
is  removed  cannot  be  returned  to  the  main  solution  without  pro- 
ducing a  permanent  precipitate  of  uranyl  ferrocyanide  the  total 
amount  of  zinc  taken  out  may  represent  a  rather  large  error. 
This  error  is  small  if  the  analyst  has  an  approximate  idea  of  the 
total  amount  of  zinc  present  and  can  safely  add  sufficient  ferro- 
cyanide to  precipitate  most  of  the  zinc  before  beginning  to  test 


DETERMINATION  OF   ZINC  265 

the  solution.  When  the  amount  present  is  entirely  unknown  it 
becomes  necessary  to  divide  the  solution  into  a  number  of  frac- 
tional parts  and  use  one  of  these  for  an  approximate  determina- 
tion, that  is,  to  titrate  by  the  addition  of  1  or  2  cc.  of  the  standard 
solution  at  a  time ;  a  second  portion  is  then  titrated  to  within  1  or 
2  cc.  of  the  required  amount  at  once  and  completed  by  the  addition 
of  0.1  cc.  at  a  time.  This  method  of  determining  an  end-point 
which  involves  the  use  of  an  " outside"  indicator  is  necessarily 
tedious  but  is  the  best  method  known  for  this  titration. 

It  is  found  that  from  0.5  to  0.7  of  the  ferrocyanide  solution 
usually  employed  must  be  added  to  200  cc.  of  water  before  a  clearly 
recognizable  test  is  produced  with  the  indicator.  If  all  titrations 
are  made  with  the  same  volume  of  solution  the  error  from  this 
source  is  constant,  and  if  all  the  solutions  titrated  contain  the 
same  amount  of  zinc  the  error  bears  the  same  relation  to  the  total 
amount  of  zinc  represented.  Suppose,  for  example,  the  ferro- 
cyanide solution  is  standardized,  by  titrating  a  solution  which  con- 
tains 0.150  gm.  of  zinc  and  has  a  volume  of  200  cc.,  and  that  30  cc. 
are  required  to  react  with  the  zinc.  The  total  volume  of  solution 
required  would  be  30.5  cc.  and  the  apparent  value  of  each  cubic 
centimeter  150  -4-  30.5,  or  0.004918.  If  now  this  solution  is  used 
to  titrate  a  zinc  solution  which  has  a  volume  of  200  cc.  and 
contains  0.05  gm.  a  volume  of  10.5  cc.  would  be  required  and 
the  calculated  amount  of  zinc  would  be  10.5  X  0.004918,  or 
0.0516  gm.  That  is,  an  error  of  1.6  mg.  results,  which  would 
have  been  avoided  if  0.5  cc.  had  been  subtracted  from  the  vol- 
umes of  ferrocyanide  solution  used  in  the  two  titrations. 

Effect  of  Varying  Temperature  Upon  the  Process.  In  the 
experiments,  the  results  of  which  are  recorded  below,  a  zinc  solu- 
tion containing  0.005  gm.  of  zinc  per  cc.  was  titrated  with  a  ferro- 
cyanide solution  containing  21.6  gm.  of  K4Fe(CN)6-3  H2O  per  liter 
at  varying  temperatures. 

The  results  show  that  altho  the  ratio  between  the  volume  of 
zinc  solution  used,  and  the  volume  of  ferrocyanide  solution  needed 


266 


QUANTITATIVE  CHEMICAL  ANALYSIS 


Vol  of 

ZnCl2  sol. 

(NH4)C1 

HCl  (cone.) 

H20 

Temp. 

K4Fe(CN)6  sol. 

cc. 

30 

gm. 

5 

cc. 
5 

cc. 
140 

Degrees 
20 

cc. 
25.5 

30 

5 

5 

140 

50-45 

29.85 

30 

5 

5 

140 

80-75 

29.85 

30 

5 

5 

140 

100-95 

30.02 

to  react  with  it,  decreases  when  the  temperature  is  increased  from 
20°  to  100°  it  is  constant  between  45°  and  85°.  In  the  practical 
use  of  this  method  it  is  very  desirable  to  adopt  among  other 
standard  conditions,  a  temperature  at  which  the  ratio  is  as  nearly 
constant  as  possible,  since  it  is  not  always  convenient  to  maintain 
a  particular  temperature  thruout  an  entire  titration.  It  should 
also  be  noted  that  at  20°  it  is  much  more  difficult  to  recognize  the 
true  end-point  than  at  any  of  the  higher  temperatures.  A  tem- 
perature of  80°  can  be  advantageously  adopted  for  one  of  the 
standard  conditions. 

Effect  of  Varying  Concentrations  on  the  Process.  The  effect 
of  varying  the  concentration  of  the  zinc  salt,  while  maintaining 
the  same  concentration  of  hydrochloric  acid  and  ammonium 
chloride,  is  shown  in  the  results  of  the  experiments  recorded  in  the 
following  table: 


ZnCl2 

(NH4)C1 

HCl  (cone.) 

H20 

Temp. 

K4Fe(CN)6  used 

cc. 

30 

gm. 
1.25 

cc. 
1.25 

CO. 

12.5 

Degrees 
80 

cc. 

29.5 

30 

2.50 

2.50 

55.0 

80 

29.70 

30 

3.75 

3.75 

97.5 

80 

29.75 

30 

5.0 

5.0 

140.0 

80 

29.80 

30 

7.50 

7.50 

225.0 

80 

30.01 

The  slight  increase  in  the  volume  of  ferrocyanide  solution  used 
with  increasing  dilution  is  undoubtedly  due  to  the  larger  amount 
of  ferrocyanide  required  to  produce  a  sufficient  concentration  of 


DETERMINATION  OF  ZINC 


267 


the  latter  to  yield  a  recognizable  test  with  the  uranium  indicator. 
There  is  no  reason  to  believe  that  the  ratio  here  concerned  varies, 
provided  the  concentration  of  the  other  reagents  remains  constant. 
Convenience  alone  should  therefore  determine  the  best  volume  to 
use  for  the  titration.  Since  in  the  actual  application  of  the 
method  the  zinc  must  usually  be  separated  from  other  metals  and 
a  large  volume  of  solution  is  necessarily  obtained  a  volume  of 
200  cc.  is  a  desirable  standard  to  adopt. 

Effect  of  the  Hydrogen  Ion  on  the  Process.  In  titrating  a 
solution  of  a  zinc  salt  with  a  solution  of  a  ferrocyanide  the  end- 
point  is  much  more  accurately  determined  when  the  solution  con- 
tains a  small  amount  of  acid  than  when  perfectly  neutral.  The 
presence  of  sufficient  acid  also  assists  in  bringing  about  the  change 
from  a  blue  flocculent  to  a  white  pulverulent  precipitate,  which  is 
a  desirable  feature.  Further,  when  lead  is  present  in  the  zinc  solu- 
tion the  presence  of  sufficient  acid  suppresses  the  formation  of 
insoluble  lead  ferrocyanide,  and  makes  it  possible  to  titrate  zinc 
in  the  presence  of  this  element. 

The  effect  of  varying  concentrations  of  hydrochloric  acid  on  the 
titration  is  shown  in  the  following  table : 


ZnClo  sol. 

(NH4)C1 

HC1  (cone.) 

H20 

Temp. 

K4Fe(CN)6  used 

cc. 

gm. 

cc. 

cc. 

Degrees 

cc. 

30 

5 

0 

145 

80 

±29.4 

30 

5 

1 

144 

80 

±29.8 

30 

5 

5 

140 

80 

29.90 

30 

5 

10 

135 

80 

30.10 

30 

5 

25 

120 

80 

31.50 

30 

5 

50 

95 

80 

32.90 

These  results  show  a  gradual  increase  in  the  volume  of  ferrocyanide 
solution  required  for  the  same  amount  of  zinc  with  increasing 
concentration  of  acid  altho  the  rate  of  increase  is  not  large.  Both 
very  large  and  very  small  amounts  of  acid  greatly  increase  the 


268  QUANTITATIVE  CHEMICAL  ANALYSIS 

difficulty  of  obtaining  accurate  end-points  and  indicate  the  de- 
sirability of  adopting  for  one  of  the  standard  conditions  5  cc.  of 
the  acid  for  each  200  cc.  of  solution. 

Preparation  and  Standardization  of  the  Solution.  This 
method  is  very  widely  used  for  the  determination  of  zinc  in  ores 
and  alloys,  and  it  is  found  desirable  to  make  1  cc.  of  the  ferro- 
cyanide  solution  used  equivalent  to  0.005  gm.  of  zinc,  that  is,  to 
prepare  it  according  to  the  unitary  rather  than  according  to  the 
normal  system.  Under  the  conditions  already  adopted  as  stand- 
ard, that  is,  where  the  temperature  at  the  beginning  of  the  titration 
is  80°,  the  volume  before  titration  is  200  cc.,  and  where  5  gm.  of 
ammonium  chloride  and  5  cc.  of  concentrated  hydrochloric  acid 
are  present  it  is  found  that  a  solution  of  potassium  ferrocyanide 
containing  21.6  gm.  of  the  crystallized  salt  per  liter  will  precipitate 
0.005  gm.  of  zinc  per  cc.  The  exact  value  of  the  solution  should 
be  determined  by  titrating  against  a  known  amount  of  zinc. 
Either  pure  metallic  zinc  or  pure  zinc  oxide,  which  has  been 
recently  ignited  to  convert  any  zinc  carbonate  which  it  may  contain 
into  zinc  oxide,  are  used  for  the  standardization. 

The  ferrocyanide  solution  is  not  a  very  stable  one  and  may  show 
an  appreciable  change  in  standard  even  after  standing  for  a  week, 
which  necessitates  frequent  restandardization.  An  appreciable 
tendency  for  the  ferrocyanide  to  change  into  ferricyanide,  which 
results  in  less  clearly  denned  end-points,  is  also  recognizable. 

II.  APPLICATION  OF  THE  METHOD  TO  THE  ANALYSIS  OF 
ZINC  ORES 

Preliminary  Statements.  Most  of  the  important  ores  of  zinc 
contain  that  element  as  sphalerite  (ZnS)  or  smithsonite  (ZnC03), 
both  of  which  are  easily  dissolved  by  concentrated  hydrochloric  acid ; 
in  certain  classes  of  ores  it  is  present  as  calamine  (Zn2SiO4-H20), 
which  is  but  slowly  or  imperfectly  decomposed  by  treat- 
ment with  acids  and  such  ores  must  usually  be  fused  with 


DETERMINATION   OF   ZINC  269 

some  basic  substance  such  as  sodium  carbonate  to  render  them 
easily  soluble. 

All  classes  of  zinc  ores  invariably  contain  silica  or  insoluble  sil- 
icates, iron  in  the  form  of  pyrites,  and  very  often  lead,  copper, 
cadmium  and  manganese,  also,  as  sulfides.  As  the  zinc  in  such 
mixtures  is  frequently  intimately  associated  with  the  other  sul- 
fides it  is  usually  necessary  to  decompose  these  minerals,  also,  in 
order  to  insure  complete  solution  of  the  zinc,  which  necesitates 
treatment  with  nitric  as  well  as  hydrochloric  acid. 

Separation  of  Zinc  in  Simple  Ores.  When  the  ore  does  not 
contain  copper  or  cadmium,  and  where  the  percentage  of  iron  is 
small  as  compared  with  the  zinc,  the  latter  can  be  separated  with 
a  sufficient  degree  of  accuracy  for  the  ferrocyanide  titration  by 
the  use  of  ammonium  hydroxide  and  bromine.  The  separation 
of  zinc  from  iron  by  the  use  of  ammonium  hydroxide  is  unsatis- 
factory, owing  to  the  occlusion  of  zinc  by  the  ferric  hydroxide 
precipitate,  but  where  the  total  amount  of  iron  does  not  exceed 
0.1  gm.  a  double  precipitation  usually  suffices  to  give  a  satis- 
factory separation.  Manganese  if  present  in  small  amounts  is 
usually  completely  precipitated  with  the  iron  as  the  dioxide,  if  a 
moderate  excess  of  bromine  water  is  also  added.  The  excess  of 
bromine  thus  added  to  the  zinc-containing  filtrate  must,  however, 
be  driven  off  by  evaporation  before  titration  with  the  ferrocyanide 
solution,  as  it  readily  oxidizes  ferrocyanide  to  ferricyanide. 

III.  OUTLINE  OF  METHOD  FOR  THE  PREPARATION  AND  STAND- 
ARDIZATION OF  THE  FERROCYANIDE  SOLUTION 

Preparation.  Weigh  out  21.63  gm.  of  crystallized  potassium 
ferrocyanide,  dissolve  in  water  and  dilute  to  1000  cc. 

Titration  of  a  Known  Weight  of  Zinc.  Ignite  about  2  gm.  of 
pure  zinc  oxide  in  a  platinum  or  porcelain  crucible  for  20  minutes 
at  a  good  red  heat  and  then  allow  to  cooL  Weigh  out  0.25  gm. 
of  the  ignited  oxide  into  a  400  cc.  beaker,  add  10  cc.  of  dilute 
hydrochloric  acid  and  warm  untill  dissolved.  Neutralize  the 


1270  QUANTITATIVE  CHEMICAL  ANALYSIS 

solution  with  ammonium  hydroxide,  add  5  cc.  of  concentrated 
hydrochloric  acid  and  then  dilute  to  200  cc.  Heat  the  solution 
thus  obtained  to  80°  and  add  somewhat  slowly  38  cc.  of  the  ferro- 
cyanide  solution.  Complete  the  titration  by  adding  the  ferro- 
cyanide  solution  in  quantities  of  not  more  than  four  drops  at  a 
time,  and  after  vigorous  stirring  bringing  a  drop  of  the  mixture 
into  contact  with  a  drop  of  a  5  per  cent  solution  of  uranium  acetate, 
which  has  been  previously  placed  on  a  wrhite  porcelain  plate  or  a 
sheet  of  glazed  white  paper.  The  drop  of  solution  taken  for  the 
test  should  be  mixed  thoroughly  with  the  drop  of  indicator,  but 
the  rod  should  be  wiped  or  rinsed  off  before  it  is  again  placed  in 
the  solution  which  is  being  titrated.  The  true  end-point  represents 
the  point  at  which  a  slight  but  clearly  denned  brownish  tinge  can 
be  recognized  with  certainty.  The  intensity  of  the  color  finally 
adopted  as  the  true  end-point  should  be  carefully  noted,  and  all 
subsequent  titrations  should  be  carried  to  the  same  color  shade. 
As  the  intensity  of  this  color  increases  on  standing,  an  effort  should 
be  made  to  allow  the  same  time  interval  to  elapse  between  the 
first  admixture  of  the  two  drops  and  the  final  decision  as  to  whether 
the  end-point  has  been  reached. 

Determination  of  Excess  Required  for  the  End-Point.  To  a 
second  beaker  add  10  cc.  of  dilute  hydrochloric  acid,  sufficient 
ammonium  hydroxide  to  neutralize  it  and  then  5  cc.  of  concen- 
trated hydrochloric  acid.  Dilute  the  mixture  to  240  cc.,  heat  to 
80°  and  titrate  with  the  ferrocyanide  solution  as  before,  noting 
that  the  absence  of  the  white  potassium-zinc  ferrocyanide  precip- 
itate may  decrease  slightly  the  excess  of  ferrocyanide  required 
to  produce  a  color  shade  as  intense  as  that  adopted  in  the  previous 
titration. 

Calculation  of  Value  of  Ferrocyanide  Solution.  Subtract  the 
volume  of  ferrocyanide  solution  used  in  this  titration  from  that 
used  in  titrating  the  zinc  solution.  Calculate  the  weight  of  zinc 
equivalent  to  the  zinc  oxide  weighed  out  and  divide  by  the  volume 
(corrected)  of  ferrocyanide  solution  used. 


DETERMINATION  OF   ZINC  271 

IV.   OUTLINE  OF  METHOD  FOR  DETERMINATION  OF  ZINC  IN  AN 
ORE  WHICH  CONTAINS  NEITHER  COPPER  NOR  CADMIUM 

Decomposition.  Weigh  out  1.5  gm.  of  the  finely  ground 
sample  into  a  200  cc.  beaker,  add  10  cc.  of  concentrated  hydro- 
chloric acid,  cover  with  a  watch  glass  and  warm  gently  until 
violent  action  ceases  and  hydrogen  sulfide  is  no  longer  given  off. 
Add  5  cc.  of  dilute  nitric  acid  and  again  warm  to  insure  complete 
decomposition  of  pyrite,  which  might  otherwise  retain  some  zinc, 
and  also  to  effect  complete  oxidization  of  all  the  iron  present. 
After  violent  action  ceases  remove  the  watch  glass  and  evaporate 
almost  to  complete  dryness,  but  avoid  a  temperature  in  excess 
of  100°. 

Separation  of  the  Zinc.  Add  to  the  residue  10  cc.  of  concen- 
trated hydrochloric  acid,  slowly  heat  to  the  boiling  point  and  then 
add  50  cc.  of  water.  Heat  the  solution  to  the  boiling  point,  add 
10  cc.  of  bromine  water  and  then  a  moderate  excess  of  ammonium 
hydroxide  and  keep  near  the  boiling  point  for  about  5  minutes. 
Allow  the  precipitate  of  iron,  manganese  and  gangue-matter  to 
settle,  then  filter  thru  a  small  filter  receiving  the  filtrate  into  a 
250  cc.  graduated  flask,  allow  to  drain  and  wash  twice  with  10  cc. 
portions  of  water.  Replace  the  graduated  flask  by  the  beaker 
just  emptied  and  pour  over  the  filter  sufficient  warm  dilute  hydro- 
chloric acid  to  change  all  of  the  ferric  hydroxide  into  ferric  chloride, 
then  wash  the  filter  free  from  iron.  Dilute  the  solution  in  the 
beaker  to  at  least  50  cc.,  heat  to  boiling  and  again  precipitate  with 
ammonium  hydroxide  and  bromine  water;  filter  and  wash  as  before, 
receiving  the  filtrate  in  the  graduated  flask  previously  used.  Add 
sufficient  hydrochloric  acid  to  this  solution  to  make  it  slightly  acid. 

Division  of  Zinc  Solution.  Cool  the  solution  in  the  flask  to 
the  temperature  of  the  room  and  dilute  with  water  until  the  liquid 
reaches  the  mark  on  the  neck  of  the  flask.  Place  a  stopper  in  the 
neck  of -the  flask  and  mix  its  contents  thoroughly  by  inverting  the 
flask  and  shaking  vigorously  several  times.  Rinse  out  a  50  cc. 


272  QUANTITATIVE  CHEMICAL  ANALYSIS 

pipet  with  some  of  the  zinc  solution  and  discard  the  solution  thus 
used;  then  measure  out  two  50  cc.  portions  of  the  solution  into 
400  cc.  beakers. 

Titration  of  Zinc.  Add  to  each  of  the  50  cc.  portions  of  zinc 
solution  5  cc.  of  concentrated  hydrochloric  acid  and  dilute  to  200 
cc.  Heat  one  of  these  solutions  to  80°  and  titrate  with  the  ferro- 
cyanide  solution  adding  10  cc.  before^  making  the  first  test  and  then 
1  cc.  portions  successively  until  an  end-point  is  reached.  Heat 
the  second  zinc  solution  to  80°  and  titrate  with  the  ferrocyanide 
solution,  adding  1  cc.  less  than  the  total  amount  used  in  the  pre- 
vious titration  before  making  the  first  test  and  then  TV  cc.  portions 
successively  until  an  end-point  is  reached.  Calculate  the  per- 
centage of  zinc  present. 

V.  QUESTIONS  AND  PROBLEMS.     SERIES  18 

1.  What  is  the  replacing  power  and  the  normal  value  of  potassium  ferro- 
cyanide, when  used  to  determine  zinc  by  the  reaction  given  on  page  263. 

2.  In  titrating  a  solution  which  has  a  Volume  of  200  cc.  and  contains  0.150 
gm.  of  zinc  30  cc.  of  ferrocyanide  solution  are  required  to  precipitate  the  zinc 
and  0.5  cc.  to  give  an  end-point  with  the  solution;  if  20.5  cc.  are  added  before 
any  tests  are  made  with  the  indicator  and  then  a  test  is  made  (necessitating 
the  removal  of  0.04  cc.)  after  each  successive  addition  of  1  cc.  portion  of  solu- 
tion, how  large  a  volume  of  ferrocyanide  solution  would  be  required  for  the 
titration? 


SECTION  VIII 

VOLUMETRIC   PROCESSES   INVOLVING   NEUTRAL- 
IZATION 


CHAPTER  XL 

GENERAL   THEORY   OF   NEUTRALIZATION  PROCESSES 

The  Reactions  Concerned.  A  large  number  of  processes, 
which  depend  upon  the  use  of  a  standard  solution  of  an  acid  or  a 
base,  are  included  in  this  group;  the  most  important  are  based 
upon  reactions  which  involve  simple  neutralization.  As  shown 
on  page  57  the  equilibrium  constants  of  such  reactions  can  be 
calculated  by  dividing  the  product  of  ka,  the  dissociation  constant 
of  the  acid,  and  kb,  the  dissociation  constant  of  the  base,  by  kw, 
the  dissociation  constant  of  water.  Since  kw  has  a  fixed  value 
and  since  either  ka  or  kfy  can  be  made  equal  to  unity  by  using  a 
strong  acid  or  base,  for  the  standard  solution  employed,  the  revers- 
ibility of  such  reactions  is  small  in  proportion  as  the  dissociation 
constant  of  the  acid  or  base  being  titrated  is  large. 

A  second  series  of  processes  of  this  group  is  based  upon  reactions 
involving  the  displacement  of  a  weak  acid  or  base  from  its  salts 
by  a  strong  acid  or  base.  It  has  been  shown  on  page  59  that  the 
constant  for  such  reactions  can  be  calculated  by  dividing  the  dis- 
sociation constant  of  the  strong  acid  or  base  used  by  the  dissocia- 
tion constant  of  the  weak  acid  or  base  of  which  the  salt  is  formed. 

The  End-Points  of  Processes  Involving  Neutralization.  The 
true  end-point  of  a  titration  in  which  a  standard  solution  of  a  base 
is  added  to  an  acid  corresponds  to  the  point  at  which  an  equivalent 

273 


274  QUANTITATIVE  CHEMICAL  ANALYSIS 

amount  of  the  acid  has  been  added,  that  is,  the  point  at  which 
the  ratio  of  the  base  added  to  the  acid  present  equals  1.  This 
ratio  is  less  than  1  if  an  insufficient  amount  of  base  has  been 
added,  and  exceeds  1  if  an  excess  has  been  added.  The  con- 
centration of  the  hydrogen  ion  in  such  mixtures  depends  upon  the 
value  of  this  ratio,  the  value  of  the  equilibrium  constant  and  the 
concentration  of  the  solution.  It  can  be  calculated  if  all  of  these 
values  are  known. 

Suppose,  for  example,  we  titrate  50  cc.  of  a  0.2  molar  solution  of 
an  acid,  whose  dissociation  constant  is  10~2,  with  a  0.2  molar  solu- 
tion of  a  strong  base  such  as  potassium  hydroxide.  The  constant 
for  the  reaction  which  takes  place  has  the  value  1  X  10~2  -r-  10~14 
=  1012.  Let  us  calculate  (H+)  after  48  cc.  of  base  have  been 
added. 

The  total  concentration  of  base  added  is  0.2  X  f-f  =  0.098, 
that  of  the  acid  added  is  0.2  X  ||  =  0.102.  Let  x  represent  the 
fraction  of  the  base  which  remains  free  and  (1  —  x)  the  fraction 
which  combines  with  the  acid.  Then  (0.098)  x  represents  the 
concentration  of  base  left  uncombined  and  0.098  (1  —  x)  the  con- 
centration of  base  which  combines  with  the  acid;  this  is  also  the 
concentration  of  the  acid  which  combines  with  the  base  and  that 
of  the  salt  formed.  Then  0.102  -  0.098  (1  -  x)  represents  the 
concentration  of  the  acid  left  uncombined.  The  law  of  mass 
action  requires  that 

(HA)  •  (KOH)  •  K  =  (KA)  •  (H20). 

Making  the  proper  substitutions  and  remembering  that  the  con- 
centration of  water  is  practically  constant,  and  can  be  disregarded, 
we  obtain: 

(0.098  x)  (0.102  -  0.098  +  0.098  x)  (1012)  =  0.098  -  0.098  x, 
or          x2  +  4.08  X  10~2  x  =  1.02  X  10~n  -  1.02  X  lO"11  x, 
from  which    x  =  3  X  10-10,     and    0.098  x  =  3  X  10~u. 


GENERAL   THEORY  OF  NEUTRALIZATION  PROCESSES     275 

Since  the  dissociation  of  the  base  at  this  concentration  is  practi- 
cally complete  3  X  1Q-11  also  represents  (H0~)  and  hence  (H+) 
must  have  the  value  10~14  -*-  3  X  10~u,  or  3.3  X  10~4. 

In  a  similar  manner  the  value  of  (H+)  after  49,  49.5,  49.7,  49.9, 
50,  50.1,  50.3,  50.5  and  51  cc.  have  been  added  can  be  calculated. 
The  results  of  these  calculations  are  represented  graphically  in 


.960 


.970 


.980  .990  1.00  1.01 

Ratio  of  Base  Added  to  Acid  Present 


1.02 


Fig.  56 — Curves  Showing  Changes  in  (H)  in  the  Titration  of  Acids 

the  second  of  the  series  of  curves  of  Fig.  56,  in  which  the  ordinates 
represent  the  common  logarithms  of  (H+)  and  the  abscissas  the 
ratio  of  base  to  acid  present  in  the  mixtures.  It  shows  that  the 
change  in  (H+)  associated  with  small  changes  in  the  value  of  this 
ratio  is  very  much  greater  in  the  neighborhood  of  the  point  at 
which  this  ratio  has  the  value  one,  than  at  those  points  at  which 
it  is  slightly  greater  or  less  than  one.  The  curve  also  shows  that 
when  this  ratio  has  the  value  1,  (H+)  has  the  value  3.16  X  10~8 
instead  of  the  value  10~7,  which  it  would  have  if  the  solution  were 


276  QUANTITATIVE  CHEMICAL  ANALYSIS 

perfectly  neutral.  This  is  due  to  the  fact  that  the  dissociation 
constant  of  the  acid  is  rather  small,  whereas  that  of  the  base  is 
large,  and  the  hydrolysis  of  the  salt  formed  yields  a  solution  in 
which  (H+)  is  much  less  than  1  X  1Q-7. 

If  next  we  calculate  a  similar  series  of  values  for  titrations  in 
which  acids  having  dissociation  constants  of  1,  10~4,  10~6,  10~8 
and  10~10  are  titrated  with  a  strong  base,  and  plot  the  results  as 
before,  we  obtain  the  series  of  curves  represented  in  the  same  figure. 
They  show  that  the  ratio  of  the  change  in  (H+)  to  the  change  in 
ratio  of  base  to  acid  decreases  as  the  dissociation  constant  of  the 
acid  decreases,  even  in  the  neighborhood  of  the  point  at  which  the 
ratio  of  base  to  acid  is  one.  When  the  dissociation  constant  of 
the  acid  is  10~10  the  curve  shows  no  inflection  at  this  point  and  the 
total  change  in  (H+)  resulting  from  a  very  large  change  in  the 
ratio  of  base  to  acid  is  extremely  small.  The  curves  also  show  that 
the  value  of  (H+)  when  this  ratio  is  1  differs  from  10~7  in  pro- 
portion as  the  dissociation  constant  of  the  acid  is  reduced. 

If  the  method  just  used  is  employed  to  ascertain  the  changes 
in  (H0~)  which  take  place  when  a  series  of  bases  are  titrated  with 
a  strong  acid,  it  will  be  found  that  the  changes  in  (H0~)  resulting 
from  a  change  in  the  ratio  of  acid  to  base  has  a  maximum  value 
in  the  neighborhood  of  the  point  at  which  the  acid  to  base  ratio 
is  one,  and  is  large  in  proportion  as  the  dissociation  constant  of 
the  base  is  large;  also  that  the  value  of  (H0~)  at  the  point  of 
which  this  ratio  is  one  differs  from  10~7,  in  proportion  as  the 
dissociation  constant  of  the  base  is  reduced. 

The  End-Points  of  Processes  Involving  Displacement.  The 
value  of  (H+)  in  a  mixture  obtained  by  adding  a  strong  acid  to  a 
salt  of  a  weak  acid  depends  upon  the  ratio  of  the  acid  added  to 
the  salt  present,  the  value  of  the  equilibrium  constant  and  the 
concentration  of  the  solution;  it  can  be  calculated  if  these  values 
are  known. 

Let  us  assume  that  a  0.2  molar  solution  of  hydrochloric  acid  is 
added  to  50  cc.  of  a  0.2  molar  solution  of  the  potassium  salt  of  an 


GENERAL  THEORY  OF  NEUTRALIZATION  PROCESSES     277 


acid  whose  dissociation  constant  has  the  value  10~10.  Since  the 
dissociation  constant  of  hydrochloric  acid  can  be  represented  by  1 
the  constant  of  the  reaction  is  1  -f-  10~10,  or  1010. 

Let  us  first  calculate  (H+)  after  48  cc.  of  strong  acid  have  been 
added.  The  total  concentration  of  this  acid  is  0.2  X  J|  =  0.098 
and  that  of  the  potassium  salt  is  0.2  X  f  £,  or  0.102.  If  x  represents 
the  fraction  of  hydrochloric  acid  left  uncombined,  0.098  x  must 
represent  the  concentration  left  uncombined,  0.098  (1  —  x)  the 
concentration  of  weak  acid  formed  and  0.102  —  0.098  (I  —  x) 
the  concentration  of  the  potassium  salt  left  uncombined.  By 
making  the  proper  substitutions  in  the  expression  representing 
the  reaction  we  obtain 

(0.098  x)  (0.102  -  0.098  +  0.098  x)  (1010)  =  0.098  (1  -  x). 

When  this  expression  is  solved  for  x  it  is  found  to  have  the  value 
2.5  X  10~8  and  0.098  x  is  2.5  X  10~9.  The  total  value  of  (H+)  is 
the  sum  of  that  due  to  the  dissociation  of  the  hydrochloric  acid, 
which  is  2.5  X  10~9,  plus  that  due  to  the  weak  acid  liberated. 
The  total  concentration  of  the  weak  acid  liberated  is  0.098  (1  -  x), 
which  can  be  calculated  to  yield  a  concentration  of  hydrogen  ion 
of  3.1  X  10~6;  hence  the 
total  value  of  (H+)  is  3.13 
X  10~6. 

The  value  of  (H+)  after 
49,  49.5,  49.7,  49.9,  50,  50.1, 
50.3,  50.5,  and  51  cc.  of  acid 
have  been  added  can  be 
calculated  in  a  similar  man- 
ner. The  results  of  these 
calculations,  also  of  similar 
calculations  in  which  the 
dissociation  constants  of  the  liberated  acids  have  the  values  10~8, 
10~6  and  10"4,  are  represented  in  the  series  of  curves  of  Fig.  57  in 
which  the  ordinates  represent  the  logarithms  of  (H+)  and  the 


Log(H) 


-2 

io~ 

4 

-4 
-6 

-&-= 

gr 

e-j 

H^ 

^^ 

I0"1 

J 

/ 

-8 

£  = 

i-o- 

0— 

,       n 

-S 

-1U 
.9 

60 

.970       .980       .990        1  00       1.01       1.02 
Ratio  of  Acid  Added  to  Salt  Present 

Fig.  57  —  Curves  Showing  Changes  in  (H) 
in  the  Titration  of  Salts. 


278  QUANTITATIVE  CHEMICAL  ANALYSIS 

abscissas  the  ratio  of  acid  added  to  the  salt  present.  They  show 
that  the  rate  at  which  (H+)  changes  in  the  neighborhood  of  the 
true  end-point,  that  is,  where  the  ratio  is  1,  is  large  where 
k  =  1Q-10,  is  quite  large  where  k  =  10~8,  is  very  small  where 
k  =  1Q-6,  and  is  scarcely  recognizable  where  k  =  10~4;  also,  that 
(H+)  at  the  true  end-point  is  much  greater  than  10~7  even  where 
k  =  10-10. 

Methods  Used  for  the  Recognition  of  End-Points.  The  end- 
points  of  titrations  which  depend  upon  reactions  involving  either 
neutralization  or  displacement  can  be  recognized  by  any  device 
which  indicates  with  sufficient  accuracy  the  changes  in  (H+)  during 
the  titration.  The  value  of  (H+)  can  be  measured  directly  by  a 
method  which  involves  the  determination  of  the  electromotive 
force  between  two  hydrogen  electrodes,  one  of  which  is  placed  in 
the  solution  being  titrated,  and  the  other  in  a  solution  contain- 
ing known  concentration  of  hydrogen  ion.* 

Advantage  may  also  be  taken  of  the  fact  that  the  rate  of  change 
in  (H+)  is  associated  with  a  change  in  the  conductivity  of  the 
mixture,  and  it  is  often  possible  to  determine  the  true  end-points 
by  measuring  the  conductivity  of  the  mixture  during  the  titration. 
Both  methods  require  the  employment  of  elaborate  and  costly 
apparatus  and  have  not  been  very  largely  used.  The  method 
commonly  employed  depends  upon  the  use  of  certain  organic 
reagents,  which  undergo  pronounced  color  changes  when  (H+) 
changes  thru  certain  definite  values. 

Reactions  of  the  Indicators  Used.  The  indicators  used  for 
this  class  of  processes  are  very  weak  acids  or  bases  and  form  salts. 
The  structural  formulae  assigned  to  the  salts  of  some  of  these 
indicators  differ  from  those  of  the  corresponding  free  acid  or  base, 
that  is,  the  formation  of  salts  is  associated  with  a  change  in  the 
position  of  one  or  more  atoms  in  the  molecule,  and  two  "tauto- 
meric"  forms  of  the  indicator  must  be  assumed  to  exist.  For 
example,  the  neutral  and  acidic  solutions  of  the  indicator  phenol- 
*  See  Hildebrand,  Jour,  of  Am.  Chem.  Soc.,  35,  (1913) 


GENERAL   THEORY  OF   NEUTRALIZATION   PROCESSES      279 

phthalein,  which  is  a  very  weak  dibasic  acid  *  are  colorless,  but 
become  deep  red  upon  the  addition  of  a  small  amount  of  base.  It 
seems  probable  that  the  color  of  the  solution  is  due  to  the  presence 
of  a  divalent  ion  which  contains  the  group  =C6H4t=0.  This 
group  is  known  to  impart  to  solutions  of  compounds  containing  it 
a  red  color,  and  is  known  as  a  "  chromophore."  The  free  acid  on 
the  other  hand  does  not  contain  this  or  any  other  chromophore, 
and  for  this  reason  neutral  or  acidic  solutions  of  the  indicator  are 
colorless.  The  transformation  of  a  colorless  into  a  colored  solu- 
tion involves  two  separate  processes.  The  first  of  these  involves 
the  ionization  of  the  indicator,  which  takes  place  in  two  stages, 
and  depends  upon  two  sets  of  equilibria,  namely 

(C6H4HO  -  C8H402  -  C»H4HO)fci  =  (CCH4HO  -  C8H402  =  C6H40)  (H) 
and 

(C6H4HO  -  C8H402  -  C6H40)  A*  =  (C6H40  -  C8H402  -  C6H40)  (H) 
The  second  depends  upon  an  equilibrium  expressed  by: 

(C6H40  -  C8H702  -  C6H40)  fcj  =  (C6H40  -  C8H402  =  C6H4  =  0) . 

If  we  multiply  the  three  equations  together  and  simplify  the 
resulting  expression  we  obtain 

.,  _  (H)2  (C6H40  -  C8H402  =  C6H4  =  0) 
(C6H4HO  -  C8H40  -  C6H4HO) 

The  value  of  K  can  be  determined  experimentally.  If  we  compare 
the  intensity  of  the  color  of  a  solution  containing  a  known  con- 
centration of  the  indicator  and  of  hydrogen  ion,  with  the  intensity 
of  the  color  of  a  solution  containing  the  same  concentration  of 
indicator  in  addition  to  sufficient  base  to  change  all  of  it  into  the 
chromophore-containing  ion,  we  can  determine  the  fraction  of 

*  Rosenstein,  Jour,  of  Am.  Chem.  Soc.,  34,  1128  (1912). 


280  QUANTITATIVE  CHEMICAL  ANALYSIS 

indicator  transformed  into  the  colored  form.     If  we  represent 
this  fraction  by  x  the  above  expression  becomes 

*  X  =  u^y 

from  which  the  value  of  K  can  be  calculated. 

This  expression  can  be  used  to  determine  the  value  of  K  for  any 
dibasic  indicator,  whose  color  is  due  to  the  divalent  ion  only.  The 
corresponding  expression  for  any  monobasic  acid  differs  from  it 
only  in  that  (H+)  replaces  (H+)2.  The  value  of  K  is  a  numerical 
expression  of  the  most  important  property*  of  this  class  of  indi- 
cators, namely,  their  tendency  to  undergo  a  color  change  in  the 
presence  of  a  definite  concentration  of  hydrogen  ion.  It  is  known 
as  the  " indicator  constant"  and  will  be  referred  to  frequently  in 
discussing  the  use  of  this  class  of  indicators. 

It  has  not  been  shown  that  all  indicators  of  this  class  undergo  a 
tautomeric  transformation.  If  there  are  indicators  of  this  class 
which  do  not  undergo  such  changes  the  color  change  is  due  to 
dissociation  alone,  and  the  value  of  K  must  then  equal  the  value 
of  the  dissociation  constant  of  the  indicator.  If,  however,  the 
value  of  K  is  always  ascertained  by  the  method  outlined,  the  theory 
of  the  cause  of  the  color  change  is  of  no  significance. 

The  Titration  of  Acids  Using  an  Acidic  Indicator.  The  gen- 
eral theory  of  indicators  outlined  in  Chapter  XXXV  can  be  used 
in  discussing  these  titrations.  The  factors  which  determine  the 
reversibility  of  the  reactions  concerned  are  the  value  of  the  indi- 
cator constant,  and  the  dissociation  constants  of  the  acid  and 
base  used. 

Let  us  assume  that  acetic  acid  (k  =  1.8  X  10~5)  is  being  titrated 
with  potassium  hydroxide  (k  =  1),  and  that  para-nitro-phenol, 
which  is  a  monobasic  acid  indicator  whose  constant  has  the  value 
*»  10~7  is  used.  As  this  indicator  is  not  known  to  undergo  a 
tautomeric  change  the  reactions  concerned  are 

*  Noyes,  Jour,  of  Am.  Chem.  Soc.,  32,  815  (1910). 


GENERAL  THEORY  OF   NEUTRALIZATION   PROCESSES      281 

(1)  C2H30(HO)+KOH-^C2H30(KO)+  ILO, 

(2)  C6H4(N02)  (HO) +KOH  -» C6H4(N02)KO  +  H20, 

(3)  C6H4(N02)KO  +C2H30(HO)-+  C6H4(N02)HO+C2H30(KO). 

Since  acidic  solutions  of  the  indicator  are  colorless  while  basic  solu- 
tions are  yellow  the  appearance  of  the  end-point  here  depends  upon 
the  concentration  of  the  C6H4NO20  ion,  and  the  process  corres- 
ponds to  the  first  of  the  two  classes  discussed  in  Chapter  XXXV. 

The  value  of  K  for  (1)  is     1  X  1.8  X  10~5  -r-  10~14  =  1.8  X  109. 

The  value  of  K  for  (2)  is     1  X  10~7  -v-lQ-14  =  107. 

The  value  of  K  for  (3)  is  1.8  X  10~5  -f-  10~7  =  1.8  X  102. 

The  values  of  K  for  (1)  and  (2)  are  sufficiently  large,  that  for  (3) 
is  too  small,  that  is,  this  reaction  is  sufficiently  reversible  to  make 
it  probable  that  a  recognizable  amount  of  the  chromophore-con- 
taining  ion  may  be  formed  before  all  of  the  acetic  acid  is  neutral- 
ized. If  a  more  weakly  acidic  indicator,  such  as  one  for  which 
k  =  10~10  is  used,  K  for  (2)  would  have  the  value  104  and  for  (3) 
1.8  X  10~5.  In  this  case  there  is  greater  danger  of  an  error  from 
the  reversibility  of  (2)  than  of  (3),  that  is,  it  might  be  necessary  to 
use  an  appreciable  excess  of  the  titrating  solution  to  produce  a 
recognizable  amount  of  the  chromophore-containing  ion.  The 
best  indicator  which  could  be  used  would  have  a  constant  of 
4.2  X  10-10  since  K  for  both  (2)  and  (3)  would  then  have  the 
value  4.2  X  10~4. 

This  discussion  makes  it  clear  that  in  the  titration  of  acids  with 
an  acidic  indicator  the  constant  of  the  indicator  used  must  be 
large,  as  compared  with  the  dissociation  constant  of  water,  but 
small  as  compared  with  the  dissociation  constant  of  the  acid  being 
titrated;  further,  if  an  indicator  whose  constant  has  a  certain 
value  is  used,  the  probability  of  obtaining  a  deferred  end-point 
on  the  one  hand,  and  of  a  premature  end-point  on  the  other  is  equal. 

The  Titration  of  Bases  with  Acidic  Indicators.  Let  us  assume 
that  ammonium  hydroxide  (k  =  1.8  X  10~5)  is  titrated  with  hydro- 


282  QUANTITATIVE  CHEMICAL  ANALYSIS 

chloric  acid  (k  =  1)  and  that  para-nitro-phenol  is  again  used  as 
the  indicator.  This  titration  corresponds  to  the  second  of  the  two 
cases  discussed  in  Chapter  XXXV.  The  reactions  concerned  are 

(4)  (NH4)HO  +  C6H4(N02)HO  -»  C6H4(NO2)  (NH4)0  +  H2O, 

(5)  (NH4)HO  +  HC1  -»  (NH4)C1  +  H20, 

(6)  C6H4(N02)(NH4)D  +  HC1  ->  C6H4(N02)HO  +  (NH4)C1. 

The  end-point  here  recognized  is  that  at  which  the  concentration 
of  the  chromophore-containing  ion  changes  from  a  recognizable 
quantity  to  one  which  cannot  be  recognized  with  certainty. 

The  value  of  K  for  (4)  is  (1Q-7)  (1.8X10-5)^1Q-14,  or  1.8  X102. 
The  value  of  tf'for  (5)  is  (1.8  X  10~5)  (1)  ^  1Q-14,  or  1.8  X  109. 
The  value  of  K  for  (6)  is  1  -^  (10-7),  or  107. 

The  values  of  K  for  (5)  and  (6)  are  sufficiently  large,  that  for  (4) 
is  too  small  to  insure  the  presence  of  a  recognizable  concentration 
of  the  chromophore-containing  ion  up  to  the  point  at  which  all  of 
the  base  has  been  neutralized.  The  best  indicator  which  could 
be  used  would  have  a  constant  of  2.4  X  10~5,  for  with  such  an 
indicator  the  value  of  K  for  both  (4)  and  (6)  would  be  4.2  X  104. 

It  is  evident  that  in  the  titration  of  bases  with  acidic  indicators 
the  indicator  constant  should  be  large  in  proportion  as  the  dis- 
sociation constant  of  the  base  being  titrated  is  small,  but  must  be 
small  as  compared  with  the  dissociation  constant  of  the  acid  used 
for  the  titration;  further,  if  an  indicator  whose  constant  has  a 
certain  value  is  used  the  probability  of  obtaining  a  deferred  end- 
point  on  the  one  hand,  and  a  premature  end-point  on  the  other 
is  equal. 

The  Use  of  Basic  Indicators.  The  indicator  constant  of  a 
basic  indicator  could  be  denned  by  an  expression  analogous  to  that 
used  for  acidic  indicators,  that  is,  by 

_  (HQ-)  (R~) 


(ROH) 


GENERAL  THEORY  OF   NATURALIZATION  PROCESSES      283 

in  which  R~  represents  the  chromophore-containing  ion.  Since 
in  any  aqueous  solution  (H+)  •  (H0~)  =  10~14  we  can  substitute 
10~14  -r  (H+)  for  (HO~)  and  obtain  an  expression  for  K  in  terms 
of  (H+)  and  the  fraction  of  indicator  transformed.  There  is  no 
objection  to  substituting  (H+)  for  10~14  -f-  (H+)  and  changing  the 
value  of  K  to  correspond  with  the  effect  of  this  substitution,  that 
is  to  define  the  indicator  constant  of  basic  indicators  the  same  as 
for  acidic  indicators.  There  is  further  no  difficulty  in  determining 
the  value  of  this  constant  in  such  a  manner  as  to  conform  to  this 
definition.  It  is  only  necessary  to  use  a  large  excess  of  acid  in- 
stead of  base  to  completely  transform  the  indicator  in  the  solu- 
tion used  as  a  standard  of  comparison  in  order  to  obtain  x,  and 
from  it  and  the  known  value  of  (H+)  to  calculate  K.  It  should 
be  noted,  however,  that  altho  the  constant  of  an  acidic  indi- 
cator varies  directly  with  its  dissociation  constant,  that  of  a 
basic  indicator  varies  inversely  with  its  dissociation  constant,  and 
hence  strongly  acidic  and  weakly  basic  indicators  show  similar 
properties. 

By  the  use  of  this  general  definition  it  becomes  unnecessary  to 
distinguish  between  acidic  and  basic  indicators,  and  the  rules 
elaborated  in  the  preceding  discussion  are  valid  for  both  classes 
of  indicators. 

Experimental  Determination  of  the  Sensitiveness  of  Indica- 
tors. According  to  the  theory  which  has.  been  elaborated  the 
properties  of  the  various  indicators  can  be  shown  most  advanta- 
geously by  arranging  them  in  a  series  with  respect  to  their  sensi- 
tiveness toward  the  hydrogen  ion.  At  one  extreme  of  the  series 
would  be  found  those  which  are  either  very  weakly  basic  or 
moderately  strongly  acidic;  .at  the  other  those  which  are  either 
very  weakly  acidic  or  moderately  strongly  basic.  A  limited 
number  of  indicators  arranged  according  to  this  plan  should  suffice 
for  the  determination  of  all  acids  and  bases,  in  so  far  as  they  can 
be  determined  by  this  class  of  methods. 

Although  the  value  of  K  represents  the  sensitiveness  of  an  indi- 


284  QUANTITATIVE  CHEMICAL  ANALYSIS 

cator  to  (H+)  it  gives  no  information  regarding  the  amount  of 
indicator  which  must  be  transformed  in  order  to  give  an  easily 
recognizable  color  change.  This  depends  upon  the  specific  char- 
acter of  the  colors  concerned,  and  the  intensity  of  the  color  which 
a  given  concentration  imparts  to  the  solution.  Hence  it  is  ad- 
vantageous to  ascertain  the  particular  value  of  (H+)  at  which  each 
indicator  of  the  series  referred  to  above  gives  a  decided  color  change 
by  an  actual  experiment.  It  is  only  necessary  to  add  a  known 
amount  of  each  indicator  to  equal  volumes  of  a  series  of  solutions 
containing  known  concentrations  of  (H+)  to  obtain  this  informa- 
tion. This  information  can  be  used  to  determine  at  least  approxi- 
mately the  value  of  (H+)  and  (H0~)  present  in  any  unknown 
solutions  when  the  concentrations  concerned  are  within  the  limits 
represented  by  the  series  of  color  changes  concerned.  It  also 
shows  the  proper  indicator  to  use  for  any  titration  if  the  value  of 
(H+)  at  the  true  end-point  has  been  calculated  by  the  method 
outlined  on  pages  274  to  277. 

A  series  of  five  indicators  arranged  in  the  order  of  increasing 
sensitiveness  toward  (H+)  is  given  in  the  following  paragraphs. 

Methyl  Orange.  This  indicator  is  the  sulfonate  of  dimethyl- 
aniline-azobenzene;  altho  the  imino  group  gives  it  weakly  basic 
properties,  its  use  as  an  indicator  probably  depends  upon  the 
strongly  acidic  sulfonic  acid  group.  It  is  used  in  the  form  of  a 
solution  which  contains  1  gm.  per  liter  of  its  sodium  salt.  When 
the  volume  of  solution  being  titrated  does  not' exceed  100  cc.  one 
drop  of  this  solution  imparts  an  easily  recognizable  yellow  color, 
which  is  not  changed  by  the  addition  of  a  base,  to  the  mixture. 
If  sufficient  acid  is  added  to  make  (H+)  equal  to  10~4  the  solution 
becomes  pink.  A  series  of  intermediate  transition  colors  begins 
to  appear  when  (H+)  =  10~5.  The  most  clearly  defined  color 
change  is  obtained  when  the  minimum  concentration  is  used  and 
at  least  80  per  cent  of  the  indicator  is  transformed.  The  value  of 
,\its  constant  is  5  X  10~4.  This  is  the  most  strongly  acidic  indi- 
cator in  general  use.  It  is  especially  useful  in  the  titration  of  very 


GENERAL   THEORY  OF   NATURALIZATION   PROCESSES      285 

weak  bases;  the  weaker  acids,  such  as  carbonic,  boric,  hydrocyanic, 
have  almost  no  effect  upon  it,  altho  large  concentrations  delay 
somewhat  the  speed  with  which  it  responds  to  changes  in  (H+). 

Cochineal.  This  indicator  is  usually  prepared  by  digesting 
the  dried  cochineal  insects  with  ten  parts  of  50  per  cent  alcohol 
and  filtering.  The  resulting  tincture  owes  its  color  to  carminic 
acid  the  structural  formula  of  which  is  not  known.  With  pure 
water  it  yields  a  ruby  red  color  which  changes  to  violet  red  upon 
the  addition  of  a  base  and  to  yellow  upon  the  addition  of  an  acid. 
The  most  decided  color  change  takes  place  when  (H+)  is  in  the 
neighborhood  of  1  X  10~5.  It  is  therefore  slightly  more  sensitive 
toward  weak  acids  and  less  toward  weak  bases  than  methyl 
orange. 

Para-nitro-phenol.  This  indicator  is  used  as  an  aqueous  solu- 
tion containing  4  gm.  per  liter.  One  drop  is  sufficient  for  titra- 
tions  in  which  the  total  volume  does  not  exceed  100  cc.  Its 
constant  has  the  value  1  X  10~7  when  20  per  cent  of  it  is  trans- 
formed. The  change  from  colorless  to  greenish-yellow  takes 
place  when  (H+)  changes  from  10~5  to  10~6. 

Rosolic  Acid.  This  is  the  anhydride  of  trioxy-triphenyl-car- 
binol.  It  is  usually  employed  in  the  form  of  an  alcoholic  solution 
which  contains  two-tenths  of  1  per  cent.  One  drop  of  this  solu- 
tion imparts  to  100  cc.  of  water  a  light  yellow  color,  which  is  not 
changed  by  the  addition  of  acids  but  becomes  violet  red  when 
(H+)  is  reduced  to  10~8.  Its  constant  has  the  value  10~8  when 
the  indicator  is  20  per  cent  transformed. 

Phenolphthalein.  This  indicator  is  prepared  by  dissolving 
2  gm.  in  a  liter  of  50  per  cent  alcohol.  One  drop  is  sufficient  for 
100  cc.  of  solution.  It  imparts  no  color  to  pure  water,  but  the 
solution  changes  to  deep  red  when  (H+)  is  changed  from  10~8  to 
10-10.  Its  constant  has  the  value  1.7  X  10~10  when  20  per  cent 
of  it  is  transformed. 


CHAPTER  XLI 

APPLICATIONS   OF  THE   METHODS   OF  ACIDIMETRY    AND 
ALKALIMETRY 

I.  DETERMINATION  OF  ACIDS  AND  ACID  SALTS 

+ 
Titration  of  Monobasic  Acids.     The  value  of  (H)  at  the  true 

end-point,  when  a  0.2  molar  solution  of  a  monobasic  acid  whose 
dissociation  constant  is  known  is  titrated  with  a  strong  base,  can 
be  inferred  with  sufficient  accuracy  from  the  data  given  by  Fig. 
56.  The  indicator  which  gives  a  pronounced  color  change  at  or 
near  this  value  can  be  ascertained  from  the  descriptions  of  the 
different  indicators  found  on  page  285.  The  accuracy  which  can 
be  attained  in  the  titration  of  acids,  even  when  the  most  favorable 
indicator  is  used,  decreases  as  the  value  of  its  dissociation  constant 
decreases. 

Titration  of  Di-  and  Tribasic  Acids.  The  theory  of  the  titra- 
tion of  these  acids  is  more  complex  since  they  dissociate  in  stages 
and  each  stage  of  the  process  is  characterized  by  a  definite  dis- 
sociation constant.  For  example  the  dissociation  of  phosphoric 
acid  is  represented  by 

(1)  (H)(H2P04)  -*-  (H3P04)  =  fci  =  1  X  10-2, 

(2)  (H)(HP04)  •*•  (H2P04)  =  fc2  =  2  X  10-7, 

(3)  (H)(P04)     -5-  (HP04)  =  ks  =  4  X  10-13. 

When  this  acid  is  titrated  with  a  base  three  different  equilibrium 
constants,  whose  values  depend  upon  the  three  dissociation  con- 
stants have  to  be  considered.  The  value  of  (H)  during  the  titra- 
tion is  determined  for  the  most  part  by  ki  up  to  the  point  at  which 

286 


ACIDIMETRY  AND  ALKALIMETRY  287 

one  equivalent  of  base  has  been  added,  by  /c2  up  to  the  point  at 
which  two  equivalents  of  base  have  been  added,  and  by  /c3  up  to 
the  point  at  which  three  equivalents  of  base  have  been  added. 
If  a  curve  similar  to  those  of  Fig.  56  is  plotted  it  will  be  found  that 
those  portions  of  it  which  are  in  the  immediate  neighborhood  of 
the  points  at  which  exactly  one  and  two  equivalents  of  base  have 

been  added  are  nearly  vertical,  that  is,  at  these  points  (H)  changes 

very  decidedly  with  slight  changes  in  the  value  of  the  ratio  of  base 

+ 
to  acid.     Experience  shows  that  the  value  of  (H)  at  the  first  of 

these  points  corresponds  approximately  to  the  value  at  which  the 
color  of  methyl  orange  changes ;  at  the  second  point  it  corresponds 
to  the  value  at  which  the  color  of  phenolphthalein  changes.  Hence 
this  acid  can  be  determined  by  using  methyl  orange  and  assuming 
that  it  is  monobasic,  or  by  using  phenolphthalein  and  assuming 
that  it  is  dibasic.  In  neither  case  are  the  end-points  very  sharply 
defined  and  the  method  yields  approximate  results  only.  The 
proper  conditions  for*  the  titration  of  all  di-  and  tribasic  acids 
can  be  indicated  if  the  dissociation  constants  of  these  acids  are 
known. 

Dissociation  Constants  of  Acids.  The  dissociation  constants 
of  some  of  the  acids  which  the  chemist  is  frequently  required  to 
determine  are  given  in  the  table  on  page  288. 

Titration  of  Acid  Salts.     When  an  acid  salt  of  a  strong  base, 

+ 

such  as  NaH2P04,  is  dissolved  in  water  the  value  of  (H)  in  the 
resulting  solution  is  determined  for  the  most  part  by  one  of  the 
dissociation  constants  of  the  acid  concerned,  in  the  illustration 
cited  by  fc2  of  phosphoric  acid.  If  such  solutions  are  titrated  with 
a  base  it  is  often  possible  to  recognize  the  point  at  which  exactly 
one  equivalent  of  base  has  been  added,  owing  to  the  very  great 
change  in  the  value  of  (H)  at  this  point.  In  the  solution  of 
NaH2P04  the  point  at  which  one  equivalent  of  base  has  been 
added  can  be  recognized  by  the  use  of  phenolphthalein,  and  the 
process  is  identical  with  that  part  of  the  titration  of  phosphoric 


288 


QUANTITATIVE  CHEMICAL  ANALYSIS 


acid  in  which  (H)  changes  from  the  first  to  the  second  of  the  two 
points  at  which  it  changes  abruptly.  The  method  is  only  appli- 
cable to  the  titration  of  acid  salts  of  strong  bases  and  a  limited 
number  of  di-  and  tribasic  acids. 

DISSOCIATION  CONSTANTS  OF  ACIDS* 


Name  of  acid 

Formula 

First  stage 

Second  stage 

Acetic 

H(C2H3O2) 

1.8    XIO"5 

Arsenic  

H3AsO4 

5X10~3 

Arsenious 

H3AsO3. 

6  XIO-10 

Boric  

H3BO3 

7  XIO-10 

Carbonic  .  . 

H2CO3 

3X10~7 

3  X10"11 

Chlorous  

HC1O 

4  X10~8 

Chloric 

HC1O3 

1 

Chromic  

H2CrO4 

1 

6X10~7 

Citric  .  .  . 

C3H4(HO)(COOH)3 

SxlO"4 

Formic  

H(COOH) 

2  14X10~4 

Hydrochloric  

HC1 

1 

Hydrocyanic  .... 

HCN 

1  3X10~9 

Hydrobromic  

HBr 

1 

Hydriodic  

HI 

1 

Hydrosulfurous  

H2S 

oxio-8^ 

1  X  10~15 

Nitrous  

HNO2 

5X10"4 

Nitric  

HNO3< 

1 

Oxalic  

(COOH)2 

3  8  X10~2 

5X10~5 

Perchloric  

HC1O4 

1 

Phosphoric  

H3PO4 

1  1X10~2 

2X10"7 

Sulfuric  .... 

H2SO4 

I 

Q  v  1  n—2 

Succinic  

C2H4(COOH)2 

6  6X10~5 

Tartaric  

C2H2(HO)2(COOH)2 

9  7X10"4 

*  Most  of  the  date  here  presented  is  from  the  table  compiled  by  Noyes,  Jour,  of  Am.  Chem. 
Soc.,  32,  860  (1910).  Some  values  are  from  Ostwald,  Zeit.  fur  Phys.  Chemie,  3,  418,  (1889) ,  or  from 
Chandler,  Jour,  of  Am.  Chem.  Soc.,  30,  713  (1908). 

II.  DETERMINATION  OF  BASES  AND  BASIC  SALTS 

Titration  of  Bases.  The  theory  of  the  titration  of  bases  is 
analogous  to  that  of  the  titration  of  acids,  but  unfortunately  the 
dissociation  constants  of  bases  have  not  been  determined  except 
in  a  few  instances.  The  dissociation  constants  of  all  the  alkaline 


ACIDIMETRY  AND  ALKALIMETRY  289 

hydroxides  are  large  and  at  moderate  concentrations  can  be  repre- 
sented approximately  by  one.  The  hydroxides  of  the  alkaline 
earths  are  but  slightly  soluble,  and  readily  change  into  oxides; 
they  are  all  dibasic  and  probably  dissociate  in  stages.  The  hy- 
droxides and  oxides  of  the  remaining  metals  are  so  insoluble  that 
they  have  no  appreciable  effect  on  the  color  of  a  solution  of  methyl 
orange.  Some  of  them,  such  as  ZnO,  can  be  determined  by  the 
method  of  back  titration,  that  is,  by  adding  a  measured  volume  of 
standard  acid  more  than  sufficient  to  react  with  the  base,  and 
titrating  the  excess  of  acid  used  with  a  standard  base. 

The  dissociation  constant  of  ammonium  hydroxide  has  the  value 
1.8  X  10~5  and  it  can  be  accurately  titrated  if  methyl  orange  or 
cochineal  is  used.  Some  of  the  substituted  ammonias,  except 
those  of  the  aromatic  group,  are  still  stronger  bases.  A  limited 
number  of  alkaloids  possess  basic  properties  strong  enough  to 
make  it  possible  to  titrate  them  directly  with  a  fair  degree  of 
accuracy. 

Titration  of  Basic  Salts.  Many  of  the  basic  salts  which  have 
been  described  are  mixtures  and  the  composition  of  many  others 
is  not  known  accurately.  Where  the  formulae  of  a  basic  salt  is 
known  it  can  frequently  be  determined  by  methods  exactly  analo- 
gous to  those  used  for  the  determination  of  acid  salts. 

III.   DETERMINATION  OF  SALTS  OF  WEAK  ACIDS  AND  BASES 
Titration  of  Salts  of  a  Weak  Acid  with  a  Strong  Acid.     The 

value  of  (H)  at  the  true  end-point,  when  a  0.2  molar  solution  of 
certain  salts  is  titrated  with  a  strong  acid,  can  be  ascertained  with 
sufficient  accuracy  from  the  data  given  in  Fig.  57.  The  proper 
indicator  to  employ  in  titrating  such  salts  can  then  be  found  by 
comparing  this  value  with  the  values  at  which  the  different  indi- 
cators show  decided  color  changes.  The  accuracy  of  such  deter- 
minations decreases  as  the  dissociation  constant  of  the  base  of 
which  the  salt  is  composed  decreases  and  the  dissociation  constant 
of  the  acid  of  which  the  base  is  composed  increases. 


290  QUANTITATIVE  CHEMICAL  ANALYSIS 

When  the  acid  of  which  the  salt  is  composed  is  di-  or  tribasic  an 
indicator  can  be  used  which  will  determine  the  point  at  which 
either  one,  two  or  three  equivalents  of  the  stronger  acid  have  been 
added.  In  the  titration  of  sodium  carbonate  for  example  the 
method  might  be  basfd  upon  one  of  two  reactions,  namely, 


(1)  NasC03+    HCl->NaHC03  +  NaCl, 

(2)  NaaCOs  +2  HC1  ->  C02  +  H20  +  2  NaCl. 

+ 
If  the  former  method  is  used  the  value  of  (H)  at  the  true  end- 

point  would  equal  that  resulting  from  the  dissociation  of  HC03 

at  the   concentration   concerned.     If  the  latter  method  is  used 

+ 
the  value  of  (H)  at  the  true  end-point  would  equal  that  resulting 

from  the  dissociation  of  H2C03  at  the  concentration  concerned, 
but  since  H2C03  breaks  down  into  C02  and  H20  this  concentration 
is  very  small.  Experience  shows  that  the  latter  method  is  much 
more  accurate  than  the  former. 

Titration  of  Salts  of  a  Weak  Base  with  a  Strong  Base.  The 
theory  of  the  titration  of  salts  which  represent  combinations  of 
very  weak  bases  and  strong  acids  is  entirely  analogous  to  that  of 
the  processes  discussed  in  the  preceding  section.  They  are  used 
for  the  titration  of  salts  of  the  aromatic  amines  and  alkaloids. 

IV.   INDIRECT  DETERMINATIONS 

Titrations  Which  Involve  a  Previous  Separation.  A  large  num- 
ber of  substances  which  cannot  be  determined  directly  by  titrat- 
ing with  an  acid  or  base  may  be  transformed  into  substances 
which  can  be  so  determined.  This  includes  a  large  number  of  the 
metallic  elements  which  form  insoluble  salts  with  weak  acids. 
Thus,  although  calcium  when  present  as  a  salt  cannot  be  titrated 
directly,  it  can  be  precipitated  from  its  solutions  as  a  carbonate, 
filtered  and  washed,  and  then  titrated  like  any  other  salt  which 
represents  a  combination  of  a  weak  acid  and  a  strong  base.  The 
accuracy  of  the  process  depends  upon  the  insolubility  of  the  precipi- 


ACIDIMETRY  AND   ALKALIMETRY  291 

tate,  upon  the  completeness  with  which  the  precipitating  agent, 
in  this  case  ammonium  carbonate,  can  be  washed  out,  and  upon 
the  accuracy  of  the  final  titration. 

Another  illustration  is  found  in  a  method  which  is  largely  used 
for  the  determination  of  phosphoric  acid  when  in  the  form  of  its 
salts.  It  is  based  upon  the  fact  that  this  acid  is,  under  proper 
conditions,  completely  precipitated  by  ammonium  molybdate  as 
(NH4)3P04'12  Mo03  which  compound  reacts  with  a  solution  of 
ammonium  hydroxide  as  shown  by  the  equation: 

(NH4)3P04-12  Mo03+24  (NH4)HO  ->  (NH4)3P04+12  (NH4)2Mo04 
+  12  H20. 

As  this  reaction  is  practically  complete  and  instantaneous  we 
can  titrate  the  Mo03  combined  with  the  ammonium  phosphate, 
and  the  amount  of  phosphorus  present  can  be  calculated  from  the 
assumption  that  every  twelve  molecules  of  Mo03  found  represent 
one  molecule  of  phosphoric  acid  originally  present. 

Titrations  Which  Involve  the  Use  of  a  Special  Reagent  to  In- 
crease Dissociation.  In  a  limited  number  of  instances  the  de- 
sired transformation  can  be  effected  by  the  use  of  a  reagent  which 
does  not  itself  react  with  the  titrating  solution,  and  in  such  de- 
terminations previous  separation  of  the  product  is  not  necessary. 
Thus  hydrocyanic  acid,  whose  acidic  properties  are  too  weak  to 
admit  of  a  direct  titration,  can  be  completely  changed  into  mer- 
curic cyanide  and  hydrochloric  acid  by  the  addition  of  mercuric 
chloride,  and  the  resulting  hydrochloric  acid  can  be  titrated  with 
accuracy.  The  process  owes  its  accuracy  to  the  remarkably  low 
dissociation  constant  of  mercuric  cyanide. 

V.  QUESTIONS  AND  PROBLEMS.    SERIES  19 

1.  A  solution  which  contains  1  gm.  of  acetic  acid  is  titrated  with  a  strong 
base,  what  is  the  value  of  (H+)  at  the  true  end-point  if  the  final  volume  is 
100  cc.? 

2  Would  you  think  it  possible  to  determine  the  following  acid  salts  by  a 
direct  titration  with  a  base;  NaHSO4,  NaHC03,  HCOOKCOO,  Na2HP04? 


292  QUANTITATIVE  CHEMICAL  ANALYSIS 

3.  Would  you  think  it  possible  to  determine  the  following  salts  by  titrating 
with  an  acid  Na(C2H3O2),  (NH4)2CO3,  K2SO3,  Na3PO4,  CaCrO4? 

4.  If  required  to  determine  the  percentage  of  H3PC>4  by  the  method  out- 
lined on  page  291,  what  value  would  you  give  to  A  of  the  general  formula  in 
calculating  the  result? 

5.  A  solution  of  formic  acid  (a  monobasic  acid  of  the  formula  H2CO2) 
which  contains  0.0046  gm.  per  liter  is  found  to  be  neutral  towards  methyl 
orange;  calculate  the  dissociation  constant  of  this  acid. 

6.  If  you  were  to  titrate  a  tenth  normal  solution  of  aniline  hydrochloride 
(C6H6(NH2)HC1)  with  a  one-tenth  normal  solution  of  sodium  hydroxide,  what 

value  should  (HO)  have  at  the  true  end-point  if  the  dissociation  constant 
of  aniline  is  4.9  X  10~10? 


CHAPTER  XLII 

THE  PREPARATION  OF  STANDARD  SOLUTIONS  OF  ACIDS  AND 

BASES 

I.   FACTORS  TO  BE  CONSIDERED 

Choice  of  the  Acid  and  Base.  As  noted  in  Chapter  XL  it  is 
essential  that  the  acids  and  bases  used  for  the  preparation  of 
standard  solutions  have  large  dissociation  constants.  It  is  also 
desirable  that  they  shall  be  stable  compounds,  that  their  action  on 
the  glass  vessels  used  to  retain  them  be  small,  and  that  they  exercise 
no  oxidizing  or  reducing  action  on  the  indicators  used.  These 
considerations  limit  the  acids  generally  used  to  hydrochloric  and 
sulfuric.  For  bases  the  hydroxides  of  sodium  and  potassium  are 
most  frequently  employed,  but  the  hydroxides  of  ammonium  and 
barium  are  sometimes  to  be  preferred. 

The  Most  Desirable  Strength.  Every  titration  should  re- 
quire the  use  of  a  moderately  large  volume  of  the  standard  solu- 
tion; hence  in  titrating  substances  of  low  percentage  composition 
either  a  large  amount  of  sample  must  be  used  or  the  concentration 
of  the  solution  used  must  be  small.  On  the  other  hand,  strong 
solutions  give  more  decisive  end-points  than  weaker  solutions 
and  their  strength  is  changed  to  a  less  extent  relatively  by  carbon 
dioxide  which  may  be  absorbed  from  the  air.  In  general  it  is  not 
desirable  to  use  solutions  of  acids  or  bases  stronger  than  one-half, 
or  weaker  than  one-tenth  normal,  altho  special  circumstances  may 
make  it  desirable  to  vary  these  limits. 

Methods  of  Preparing  Solutions.  Since  the  concentration  of 
moderately  strong  sulfuric  acid  (preferably  about  60  per  cent)  can 
be  determined  with  very  great  accuracy  from  its  specific  gravity 

293 


294  QUANTITATIVE  CHEMICAL  ANALYSIS 

(see  Chapter  XLIX)  a  standard  solution  of  this  acid  can  be  pre- 
pared by  diluting  a  weighed  amount  to  the  calculated  volume. 
Similarly  a  standard  solution  of  hydrochloric  acid  can  be  pre- 
pared by  passing  pure  dry  hydrochloric  acid  gas  into  a  flask 
containing  a  weighed  amount  of  water,  determining  the  increase 
in  the  weight  of  the  flask  and  diluting  the  solution  to  the  calcu- 
lated volume. 

An  indirect  method  in  which  a  solution  of  approximately  the 
desired  strength  is  first  prepared,  its  strength  accurately  deter- 
mined by  an  independent  process,  and  then  diluted  to  the  calcu- 
lated volume  is  often  preferable.  The  exact  value  of  the  diluted 
solution  can  be  determined  by  a  gravimetric  process  or  by  titrating 
against  a  known  weight  of  some  pure  substance  with  which  the 
solution  reacts  completely.  A  large  number  of  such  substances 
have  been  proposed  and  are  used  by  different  chemists  for  this 
purpose. 

Sodium  carbonate  can  usually  be  obtained  sufficiently  pure, 
except  for  small  amounts  of  water  and  bicarbonate;  if  heated  to 
300°  in  a  platinum  crucible  for  a  few  minutes  it  gives  the  pure 
normal  carbonate  which  can  be  weighed  accurately  and  titrated 
against  solutions  of  mineral  acids  using  methyl  orange  as  the 
indicator. 

Calcium  carbonate  in  the  form  of  finely  ground  calc-spar  is  also 
to  be  had  in  a  very  high  degree  of  purity,  and  can  be  used  like  the 
sodium  compound. 

Borax  (Na2B407-10  H20)  is  readily  obtained  pure  by  recrystalli- 
zation  at  temperatures  below  50°  and  also  gives  accurate  results 
in  the  standardization  of  acids. 

Succinic  and  benzoic  acids  can  also  be  prepared  in  a  high  degree 
of  purity  and  offer  simple  and  accurate  methods  for  the  standard- 
ization of  alkaline  solutions. 


SOLUTIONS  OF  ACIDS  AND  BASES 


295 


II.   OUTLINE  OF  METHOD  FOR  THE  PREPARATION  OF  SEMI- 
NORMAL  ACID  AND  ALKALI 

Preparation  of  Solutions.  Weigh  out  ou  a  rough  balance;  50 
gm.  of  pure  sodium  hydroxide,  place  in  a  2500  cc.  flask,  add  ^liters 
of  distilled  water  and  shake  occasionally  until  the  alkali  is  com- 
pletely dissolved,  Next  add  about  5  gm.  of  finely  powdered  C.  P. 
calcium  oxide  and  allow  the  mixture  to  stand  for  an  hour  with 
occasional  shaking,  or  still  better  allow  it  to  stand 
over  night.  Place  a  Witt  filter-plate  in  a  filtering 
tube  and  provide  with  a  good  thickness  of  washed 
asbestos  in  the  customary  manner;  connect  the 
filter  tube  with  a  clean  two-liter  bottle  as  shown 
in  Fig.  58  and  filter  the  alkali  solution  into  the 
bottle.  Keep  the  bottle  stoppered  as  far  as 
possible.  t^^J^^T^L 

Measure  out  100  cc.  of  concentrated  C.  P. 
hydrochloric  acid  into  a  clean  two-liter  fieltfc, 
dilute  to  2  liters  with  water  which  is  free  from 
carbon  dioxide  and  mix  thoroughly.  To  deter- 
mine whether  the  carbon  dioxide  is  present  in 
objectionable  amounts  add  one  drop  of  phenol- 
phthalein  indicator  to  200  cc.  of  the  water  in 
question,  and  then  one  drop  of  the  approximately 
semi-normal  alkali  solution;  if  the  mixture  does  not  acquire  a 
distinct  pink  color  the  amount  of  carbon  dioxide  is  excessive,  and 
the  water  must  be  heated  to  the  boiling  point  to  remove  it... 

Determination  of  the  Volumetric  Ratio.  Measure  out  a  25  cc. 
pipet  full  of  the  acid  solution  into  a  200  cc.  beaker  or  Erlenmeyer 
flask,  dilute  to  50  cc.  and  add  a  drop  of  methyl  orange  indicator. 
Place  a  piece  of  white  paper  under  the  vessel  and  then  add  the 
alkali  solution  from  a  buret  until  the  mixture,  after  passing  thru  a 
series  of  color  shades,  finally  changes  permanently  to  a  clear  lemon 
yellow.  The  color  shade  finally  obtained  should  correspond  to 


Fig.  58.  —  Device 
for  Filtering  Al- 
kali Solution. 


296  QUANTITATIVE  CHEMICAL  ANALYSIS 

that  which  results  from  the  addition  of  one  drop  of  the  indicator 
to  75  cc.  of  water.  Repeat  this  determination  until  the  results  of 
successive  determinations  do  not  differ  by  more  than  one  part  in 
five  hundred.  From  the  average  of  the  results  finally  accepted, 
that  is,  those  which  are  believed  to  involve  no  large  errors,  cal- 
culate the  volumetric  ratio  of  the  two  solutions  by  dividing  the 
volume  of  alkali  solution  used  by  the  volume  of  acid  solution 
used. 

Titration  Against  Pure  Calcium  Carbonate.  Weigh  out  0.8 
gm.  of  pure  and  recently  dried  calcium  carbonate  into  a  300  cc. 
beaker,  cover  with  a  watch  glass  and  introduce  50  cc.  of  the  acid 
solution  measured  preferably  from  a  pipet.  Agitate  the  contents 
of  the  beaker  until  the  carbonate  is  completely  dissolved,  then 
warm  gently  to  a  temperature  not  exceeding  60°  for  the  purpose 
of  expelling  the  large  excess  of  carbon  dioxide.  Rinse  off  the 
under  side  of  the  watch  glass  and  the  sides  of  the  beaker  with  25 
cc.  of  water,  add  a  drop  of  methyl  orange  indicator  and  titrate  as  in 
the  determination  of  the  volumetric  ratio. 

Calculation  of  Strength  of  the  Two  Solutions.  Calculate  the 
volume  of  acid  solution  equivalent  to  the  volume  of  alkali  solu- 
tion used  in  the  last  titration  by  dividing  by  the  volumetric  ratio, 
and  subtract  the  quotient  from  the  volume  of  acid  solution  used. 
Calculate  the  weight  of  hydrochloric  acid  theoretically  required 
to  react  with  the  calcium  carbonate  weighed  out,  and  divide  by 
the  volume  of  acid  solution  found  to  be  equivalent  to  it  in  the 
previous  calculation;  the  quotient  represents  the  weight  of  hydro- 
chloric acid  present  in  1  cc.  of  the  solution.  Repeat  the  standard- 
ization with  a  second  portion  of  calcium  carbonate  or  until  results 
are  obtained  which  do  not  differ  by  more  than  one  part  in  500. 

Calculate  the  weight  of  sodium  hydroxide  needed  to  neutralize 
the  hydrochloric  acid  in  1  cc.  of  the  original  undiluted  solution  of 
that  reagent  and  divide  by  the  volumetric  ratio;  the  quotient 
represents  the  weight  of  sodium  hydroxide  present  in  1  cc.  of  the 
alkali  solution. 


SOLUTIONS  OF  ACIDS  AND  BASES  297 

Reduction  to  Semi-normal  Strength.  Calculate  the  volume  to 
which  1500  cc.  or  some  other  convenient  volume,  of  the  solution 
should  be  diluted  to  make  each  cubic  centimeter  contain  exactly 
0.01823  gm.  and  add  the  necessary  amount  of  water,  assuming  that 
neither  contraction  nor  expansion  takes  place.  In  making  this 
dilution  first  rinse  out  a  1000  cc.  and  a  500  cc.  flask  with  a  little  of 
the  acid  solution  and  discard;  then  fill  the  flasks  to  the  mark  with 
the  solution  and  discard  whatever  remains  in  the  bottle,  but  do  not 
rinse  the  latter  with  water;  next  drain  the  contents  of  the  two 
flasks  into  the  bottle  and  add  the  calculated  amount  of  water 
which  should  be  measured  accurately  from  a  buret. 

Dilute  in  a  similar  manner  the  alkali  solution  to  semi-normal 
strength,  that  is,  so  that  each  cubic  centimeter  contains  exactly 
0.020  gm. 

Checking  Work.  Redetermine  the  volumetric  ratio  between 
the  two  solutions;  if  it  differs  from  one  by  more  than  two  parts 
in  one  thousand  faulty  work  has  been  done  and,  since  the  error 
may  be  in  either  one  or  both  of  the  two  solutions,  the  standardiza- 
tion with  pure  calcium  carbonate  must  then  be  repeated.  If 
difficulty  is  experienced  in  attaining  the  requisite  accuracy  by  this 
method  standardize  the  acid  solution  by  the  gravimetric  method 
described  below.  If  either  of  the  solutions  has  been  diluted  to 
below  semi-normal  strength  it  is  not  necessary  to  prepare  a  new 
solution,  but  the  exact  factor  representing  the  relation  of  the 
solution  to  normal  strength  should  be  calculated  and  used  in  place 
of  the  factor  one-half  wherever  this  factor  would  have  been  used. 

Gravimetric  Method  of  Standardization.  Remove  with  a 
pipet  25  cc.  of  the  acid  solution,  dilute  to  200  cc.  and  add  a  slight* 
excess,  that  is,  about  10  per  cent  more  silver  nitrate  than  is  theoret- 
ically required  to  react  with  the  chlorine  present.  Heat  the 
mixture  to  boiling  and  stir  until  the  precipitate  coagulates,  then 
filter  on  an  asbestos  filter,  wash  dry  and  weigh  resulting  silver 
chloride.  Calculate  the  relation  of  the  acid  solution  to  normal 
strength  from  the  weight  of  silver  chloride  obtained  from  each 


298  QUANTITATIVE  CHEMICAL  ANALYSIS 

cubic  centimeter  of  acid  measured  out.  Calculate  the  relation  of 
the  alkali  solution  to  normal  strength  from  the  volumetric  ratio 
and  the  normal  value  of  the  acid  solution. 

III.   EXPERIMENTS  WITH  INDICATORS 

Prepare  one-tenth  normal  solutions  of  acid  and  alkali  by  diluting 
50  cc.  portions  of  the  semi-normal  solutions  already  prepared  to 
exactly  250  cc.  Remove  by  means  of  a  pipet  10  cc.  of  the  one-tenth 
normal  acid  solution  to  a  200  cc.  beaker  or  Erlenmeyer  flask,  add 
80  cc.  of  water,  a  drop  of  methyl  orange  indicator  and  titrate 
with  the  tenth  normal  alkali.  Note  and  record  all  of  the  shades 
of  color  thru  which  the  solution  passes,  the  color  when  an  equiva- 
lent amount  of  alkali  has  been  added,  the  amount  of  alkali  needed 
to  bring  about  the  most  pronounced  color  change  and  the  color 
when  an  excess  of  alkali  has  been  added.  Next  pass  a  stream  of 
carbon  dioxide,  which  has  been  washed  free  from  other  acids,  thru 
the  solution  and  note  the  effect,  if  any,  on  the  color  of  the  solution. 

Perform  a  similar  series  of  experiments  with  the  indicators, 
cochineal,  rosolic  acid,  para-nitro-phenol  and  phenolphthalein. 

IV.   QUESTIONS  AND  PROBLEMS.     SERIES  20 

1.  If  the  water  used  in  preparing  the  standard  acid  had  been  saturated 
with  carbon  dioxide,  how  and  under  what  conditions  wrould  it  have  affected 
the  results  obtained  with  this  solution? 

2.  If  the  calcium  carbonate  used  had  contained  one  per  cent  of  calcium 
oxide,  how  would  the  results  obtained  with  the  standard  acid  and  standard 
base  be  affected? 

3.  A  solution  of  sulfuric  acid  is  prepared  by  weighing  out  5  gm.  of  pure 
CuSO4'5  H2O,  dissolving  in  water,  and  precipitating  the  copper  by  electroly- 
sis; if  this  solution  is  diluted  to  1000  cc.,  what  relation  does  it  bear  to  normal? 

4.  How  would  you  prepare  a  liter  of  solution  in  which  (H)  =  1  X  10~3 
.    from  80  per  cent  acetic  acid  assuming  its  dissociation  constant  is  1.8  X  10~5? 


CHAPTER  XLIII 

DETERMINATIONS  WITH  A  STANDARD  ACID  AND  A  STANDARD 

BASE 

14,  DETERMINATION  OF  THE  STRENGTH  OF  CONCENTRATED 
SULFURIC  ACID 

Outline  of  the  Method.  Weigh  accurately  a  clean  glass- 
stoppered  weighing  bottle  of  about  10  cc.  capacity.  Prepare  a 
clean  and  dry  dropping-tube  or  pipet  of  about  3  cc.  capacity;  in- 
sert into  the  bottle  containing  the  sample  and  fill  about  half  full. 
Remove  from  the  bottle  and  allow  about  15  drops  to  flow  into  the 
weighing  bottle,  being  very  careful  to  avoid  spattering,  then  close 
the  bottle  and  weigh  accurately.  Fill  the  bottle  nearly  full  of 
water,  mix  and  pour  into  a  200  cc.  beaker,  then  rinse  out  at 
least  three  times  with  10  cc.  portions  of  water.  Add  a  drop  of 
any  desired  indicator  and  titrate  with  the  standard  alkali  solu- 
tion. Calculate  the  percentage  of  H2S04  by  the  use  of  the  general 
formula. 

II.   DETERMINATION  OF  THE  ACIDITY  OF  VINEGAR 

Preliminary  Statements.  The  acidity  of  vinegar,  unless  adul- 
terated with  sulfuric  acid,  is  due  almost  entirely  to  acetic  acid. 
When  titrated  with  a  base  the  coloring  matter  present  undergoes 
a  gradual  color  change  which  is  difficult  to  characterize;  this 
change  can  be  distinguished  with  fair  accuracy  from  the  color 
change  of  phenolphthalein  if  a  large  amount  of  the  indicator  is 
added  and  the  solution  diluted  sufficiently.  In  extreme  cases, 
that  is,  where  the  color  is  very  intense,  it  may  be  necessary  to 
remove  it  by  the  addition  of  bone  black  and  filtering,  but  since 
this  reagent  absorbs  small  amounts  of  acid  its  use  should  if 

299 


300  QUANTITATIVE  CHEMICAL  ANALYSIS 

possible  be  avoided.  It  is  customary  to  report  results  in  terms 
of  the  total  weight  of  acid,  calculated  as  acetic,  per  cubic  centi- 
meter of  sample. 

Outline  of  Method.  Measure  out  10  cc.  of  the  vinegar  into  a 
400  cc.  beaker  and  dilute  with  200  cc.  'of  water  free  from  carbon 
dioxide.  Add  three  drops  of  phenolphthalein  and  titrate  with 
the  alkali  solution,  disregarding  the  changes  from  brown  to  drab 
and  endeavoring  to  recognize  the  point  at  which  the  pink  of  the 
phenolphthalein,  modified  to  some  extent  by.the  drab  color  of  the 
vinegar,  becomes  apparent.  Calculate  the  weight  of  acetic  acid 
in  1  cc.  of  sample. 

III.   DETERMINATION  OF  POTASSIUM  BITARTRATE  IN  ARGOL 
OR  COMMERCIAL  CREAM  OF  TARTAR 

Preliminary  Statements.  The  chief  source  of  cream  of  tartar 
and  tartaric  acid  is  the  argol  which  separates  on  the  sides  of  the 
casks  during  the  manufacture  of  wine.  It  contains  in  addition 
to  potassium  bitartrate  (CJEI^KOe)  salts  of  a  number  of  organic 
acids  and  large  amounts  of  coloring  matter.  The  dissociation 
constant  of  the  first  hydrogen  atom  of  tartaric  acid  is  9.7  X  10~4, 
but  as  two  equivalents  of  base  must  be  added  to  a  solution  of  this 
acid,  to  give  a  red  color  with  phenolphthalein,  the  dissociation 
constant  of  the  second  hydrogen  atom  must  greatly  exceed  that 
of  phenolphthalein  and  therefore  potassium  bitartrate  is  one  of 
the  acid  salts  which  can  be  titrated  directly. 

The  large  amount  of  coloring  matter  present  in  argol  often  make 
it  difficult  to  recognize  the  true  end-point;  the  conditions  ob- 
served in  the  titration  of  vinegar  also  apply  here. 

Outline  of  the  Method.  Weigh  out  2  gm.  of  the  finely  pow- 
dered sample,  add  150  cc.  of  hot  water  and  stir  for  a  few  minutes. 
If  a  large  amount  of  insoluble  matter  remains,  filter  on  a  small  filter 
and  wash  with  hot  water  until  the  washings  are  free  from  acidity. 
Add  three  drops  of  phenolphthalein  and  titrate  with  the  standard 
alkali  solution.  Calculate  the  percentage  of  potassium  bitartrate. 


A  STANDARD   ACID   AND  A   STANDARD   BASE          301 

IV.   DETERMINATION  OF  BORIC  ANHYDRIDE  IN  NATURAL  BORATES 

Theory  of  the  Method.  The  naturally  occurring  borates, 
which  include  the  minerals  colemanite,  ulexite  and  pandermite, 
are  simple  or  double  borates  of  calcium  and  sodium.  They  are 
usually  associated  with  the  carbonates  and  sulfates  of  the  alkali 
metals  and  with  clay  and  sand.  As  they  are  the  source  of  most 
of  the  borax  and  boric  acid  of  commerce  the  value  of  ores  contain- 
ing them  depends  upon  the  percentage  of  boric  anhydride  which 
they  contain. 

The  dissociation  constant  of  boric  acid  is  so  small  that  it  is 
completely  displaced  from  solutions  of  its  salts  by  an  equivalent 
amount  of  a  strong  acid;  if  the  salts  are  insoluble  an  excess  of  the 
acid  must  be  used.  Even  concentrated  solutions  of  boric  acid  do 
not  affect  the  color  of  methyl  orange  and  hence  this  indicator  can 
be  used  to  determine  the  point  at  which  all  of  the  mineral  acid  but 
none  of  the  boric  acid  in  a  mixture  which  contains  both  has  been 
neutralized.  Hence  if  a  sample  which  contains  any  of  the  borates 
named  is  treated  with  an  excess  of  hydrochloric  acid  and  the 
mixture  made  to  give  a  neutral  reaction  with  methyl  orange  it  will 
contain  an  amount  of  free  boric  acid  which  corresponds  to  the 
boric  anhydride  present.  The  free  acid  cannot  be  titrated  directly 
even  where  phenolphthalein  is  used,  but  the  addition  of  glycerine 
or  mannitol  increases  its  acidic  properties  to  such  an  extent  that 
this  titration  then  becomes  possible.  If  glycerine  is  used  it  must 
form  about  30  per  cent  by  volume  of  the  entire  mixture;  if  manni- 
tol is  used  2  per  cent  by  weight  is  sufficient,  and  the  end-point  is 
more  sharply  defined. 

The  method  is  not  affected  by  the  presence  of  carbonates  if  the 
carbon  dioxide  which  is  liberated  during  the  decomposition  of  the 
sample  is  expelled,  but  since  boric  acid  is  very  slightly  volatile 
long  boiling  must  be  avoided.  The  accuracy  of  the  method  depends 
largely  upon  the  maintenance  of  the  proper  concentration  of  the 
reagents  used. 


302  QUANTITATIVE  CHEMICAL  ANALYSIS 

Outline  of  the  Method.  Weigh  out  1.5  gm.  of  the  finely 
ground  sample  into  a  200  cc.  beaker,  add  5  cc.  of  dilute  hydro- 
chloric acid,  warm  gently  and  stir  with  a  glass  rod  until  the  sapiple 
seems  to  be  completely  decomposed,  then  add  10  cc.  of  water  and 
heat  to  80°.  If  a  large  amount  of  flocculent  residue  remains,  filter 
on  a  very  small  filter  but  keep  the  volume  of  filtrate  and  washings 
to  about  50  cc.  Add  a  drop  of  methyl  orange  and  then  standard 
sodium  hydroxide  until  the  mixture  has  a  clear  lemon  yellow  color. 
Next  add  a  drop  of  phenolphthalein  and  about  1  gm.  of  mannitol 
and  finally  titrate  with  the  standard  alkali  to  a  permanent  pink 
color.  Add  another  half  gram  of  mannitol  and  if  the  color  fades 
continue  adding  alkali  until  it  is  restored.  As  equilibrium  is 
attained  but  slowly  more  time  should  be  allowed  for  this  titration 
than  for  those  previously  described.  Calculate  the  percentage  of 
B2O3,  assuming  that  each  molecule  has  a  neutralizing  power  of  two. 

V.  THE  ANALYSIS  OF  COMMERCIAL  ALKALIES 

Preliminary  Statements.  The  alkalies  of  commerce  consist 
mainly  of  the  hydroxides,  carbonates  and  bicarbonates  of  sodium 
and  potassium.  Their  total  alkalinity  can  be  accurately  deter- 
mined by  a  direct  titration  with  a  standard  acid,  using  methyl 
orange  as  indicator;  or,  by  using  the  process  of  back  titration  and 
heating  the  solution  to  drive  off  carbon  dioxide,  other  indicators 
may  be  used.  It  is  sometimes  necessary  to  distinguish  between 
the  alkalinity  due  to  hydroxides  and  carbonates  or  between  that 
due  to  carbonates  and  bicarbonates. 

Methods  for  the  Determination  of  Hydroxides  and  Carbon- 
ates. If  a  solution  which  contains  both  hydroxides  and  carbon- 
ates is  titrated  with  a  standard  acid,  using  phenolphthalein,  the 
color  change  takes  place  when  the  hydroxide  has  been  completely 
neutralized  and  the  carbonate  changed  into  bicarbonate;  hence 
the  difference  between  the  result  obtained  for  total  alkalinity  and 
that  obtained  by  this  method  represents  the  acid  needed  to  neu- 
tralize the  bicarbonate  formed  from  the  normal  carbonate  origi- 


A  STANDARD  ACID  AND  A  STANDARD   BASE          303 

nally  present  and  it  is  possible  to  calculate  both  the  hydroxide  and 
carbonate  originally  present.  As  the  end-point  in  the  latter 
titration  is  very  unsatisfactory,  this  method  is  used  only  for  ap- 
proximate determinations. 

A  more  satisfactory  method  of  making  this  determination  de- 
pends upon  the  addition  of  sufficient  barium  chloride  to  precipitate 
all  of  the  carbonate  and  titration  of  the  hydroxide  in  the  resulting 
mixture. 

Outline  of  Method  for  the  Determination  of  the  Hydroxide 
and  Carbonate  of  Soda  in  Commercial  Caustic  Soda.  Weigh 
accurately  a  glass  weighing  bottle  of  about  10  cc.  capacity  and 
transfer  to  it  as  rapidly  as  possible  about  10  gm.  of  the  roughly 
powdered  and  mixed  sample,  and  again  weigh  accurately.  Empty 
into  a  small  beaker,  add  about  50  cc.  of  carbon-dioxide-free  water 
and  stir  until  the  sample  is  dissolved.  Pour  into  a  250  cc.  grad- 
uated flask  and  rinse  out  both  bottle  and  beaker  with  more  water, 
cool  to  the  normal  temperature,  dilute  to  exactly  250  cc.  and  mix 
thoroughly.  The  very  small  amount  of  insoluble  residue  some- 
times found  may  be  allowed  to  settle  and  is  disregarded. 

Measure  out  25  cc.  of  the  solution,  add  50  cc.  of  water,  a  drop  of 
methyl  orange  and  titrate  with  the  standard  acid.  Remove  a 
second  25  cc.  portion,  add  50  cc.  of  water,  5  cc.  of  reagent  barium 
chloride,  a  drop  of  phenolphthalein  and  titrate  with  the  standard 
acid,  adding  the  latter  very  slowly  as  the  titration  approaches 
completion.  Calculate  the  percentages  of  sodium  hydroxide  and 
sodium  carbonate  present. 

VI.   DETERMINATION  OF  CRUDE  PROTEIN  IN  FLOUR 

Theory  of  the  Method.  The  proteins  represent  a  group  of 
extremely  complex  nitrogen-containing  compounds,  which  form 
one  of  the  three  classes  of  nutrient  materials  present  in  foods. 
Altho  the  percentage  of  nitrogen  present  varies  somewhat,  experi- 
ence has  shown  that  protein  can  be  determined  with  fair  accuracy 
by  multiplying  the  percentage  of  nitrogen  present  by  5.7.  Since  the 


304  QUANTITATIVE   CHEMICAL  ANALYSIS 

correct  value  of  this  factor  varies  somewhat,  and  since  very  small 
amounts  of  nitrogen-containing  substances  which  are  not  true 
proteids  may  be  present,  the  results  obtained  by  this  method  are 
always  designated  as  "  crude  protein.'7 

When  flour  is  heated  with  concentrated  sulfuric  acid  it  is  slowly 
reduced;  the  carbon  and  hydrogen  of  the  flour  are  oxidized  to  car- 
bon dioxide  and  water  and  the  nitrogen  is  changed  to  ammonium 
sulfate.  When  the  resulting  solution  is  distilled  with  an  excess  of 
a  strong  base  ammonia  is  formed  and  distills  over  and  can  then  be 
determined  by  titrating  with  a  standard  acid.  Under  certain 
conditions  these  operations  can  be  carried  out  quantitatively,  and 
form  the  basis  of  the  Kjeldahl  method  which,  with  its  various 
modifications,  is  used  for  the  determination  of  all  classes  of  nitro- 
gen-containing compounds. 

Outline  of  Method  of  Procedure.  Weigh  out  about  2  gm.  of 
the  sample  into  a  500  cc.  Kjeldahl  flask,  which  should  be  made  of 
hard  glass.  Add  20  cc.  of  concentrated  sulfuric  acid,  using  it  to 
rinse  down  any  particles  of  the  sample  which  adhere  to  the  sides 
of  the  flask,  and  then  add  about  0.7  gm.  of  mercuric  oxide  for  the 
purpose  of  increasing  the  speed  of  the  reaction.  Place  the  flask 
in  an  inclined  position  on  a  cold  sand  bath  and  heat  gently  for 
ten  minutes  or  until  violent  frothing  ceases,  then  raise  the  tem- 
perature to  the  boiling  point  and  boil  vigorously  until  a  color- 
less solution  is  obtained.  Remove  from  the  rack,  allow  to  cool 
slightly,  and  add  a  few  grains  of  solid  potassium  permanganate, 
using  sufficient  to  produce  a  slight  but  permanent  pink  or  green 
color.  Allow  to  cool,  dilute  to  200  cc.  and  again  cool  under  the 
tap  to  the  temperature  of  the  room. 

Add  to  the  receiver  of  a  distilling  apparatus  10  cc.  of  semi- 
normal  hydrochloric  acid,  50  cc.  of  water  and  one  drop  of  methyl 
orange.  Place  the  delivery  tube  attached  to  the  distillation 
apparatus  inside  the  receiver  and  adjust  the  level  of  the  latter 
until  the  end  of  the  delivery  tube  touches  the  surface  of  the  liquid 
in  the  receiver. 


A  STANDARD   ACID  AND   A  STANDARD   BASE          305 

Add  to  the  solution  in  the  Kjeldahl  flask  50  cc.  of  a  50  per  cent 
solution  of  sodium  hydroxide,  then  10  cc.  of  a  5  per  cent  solution 
of  potassium  sulfide  (to  precipitate  the  mercury)  and  2  gm.  of 
granulated  zinc  (to  prevent  boiling  over)  and  at  once  connect 
with  the  still-head  by  means  of  a  good  rubber  stopper. 

Heat  to  boiling  and  continue  distilling  until  the  volume  of  the 
solution  in  the  receiver  amounts  to  200  cc.  Remove  the  receiver, 
rinse  out  the  delivery  tube  and  titrate  with  a  one-tenth  normal 
solution  of  ammonium  hydroxide.  Calculate  and  report  the  per- 
centage of  crude  protein  present. 

VII.   QUESTIONS  AND  PROBLEMS.     SERIES  21 

1.  Calculate  by  the  general  formula  the  percentage  of  citric  acid,  a  tri- 
basic  acid  of  the  formula  CeHsOr,  from  the  following  data: 

Weight  of  mixture  used,  0.643  gm. 

Volume  of  KOH  solution  used  for  the  titration  31  cc. 

1  cc.  of  KOH  solution  =  0.015  gm.  of  pure  oxalic  acid  (C2H*Os-2  H2O). 

<!V*l*y 

2.  Calculate  the  percentage  of  P2O5  in  a  solution  of  H3PO4  from  the  follow- 
ing data: 

Weight  of  solution  used,  6.43  gm. 

Volume  of  KOH  solution  used  for  the  titration  (with  methyl  orange) 

26  CC.       ^Vw>ry^  4~^    o-*^  ^  ~^d*       H  (  ^ 

1  cc.  of  KOH  solution  contained  0.016  gm. 

3.  Show  how  B2O3  could  be  determined  in  pure  borax  more  easily  than  in 
calcium  borate. 

4.  Explain  why  the  BaCO3  precipitated  in  the  analysis  of  caustic  soda 
has  no  effect  on  the  titration.     Is  there  any  objection  to  using  methyl  orange 
for  the  titration?     Is  there  any  objection  to  filtering  off  and  washing  the 
BaCOs  precipitate? 

5.  Calculate   by  the  simplest  method  the  volume  of  semi-normal  acid 
required  to  neutralize  the  ammonium  hydroxide  produced  by  distilling  1  gm. 
of  FeSO4(NH4)2SO4-6  H2O  with  an  excess  of  KOH. 

6.  How  would  you  prepare  a  solution  of  HC1  so  that  each  cubic  centimeter 
should  equal  exactly  0.01  gm.  of  NaNOs,  when  the  latter  was  determined  by 
reducing  to  an  ammonium  salt,  distilling  with  an  excess  of  KOH  and  titrat- 
ing the  distillate  with  the  HC1  solution? 


SECTION   IX 
VOLUMETRIC  PROCESSES  INVOLVING   OXIDATION 


CHAPTER  XLIV 

GENERAL  FEATURES  OF  PROCESSES   INVOLVING   OXIDATION 

Definition  of  Oxidation  and  Reduction.  The  term  oxidation 
is  here  used  in  its  broadest  sense  and  includes  all  changes  in  which 
any  negative  element  or  radical  is  added  to,  or  any  positive  ele- 
ment or  radical  is  removed  from,  the  substance  under  consideration. 
Reduction  represents  the  converse  of  this  and  the  two  actions  are 
necessarily  reciprocal,  that  is,  where  one  element  is  oxidized  some 
other  must  be  reduced,  and  the  total  amount  of  oxidation  effected 
must  be  equivalent  to  the  total  amount  of  reduction  effected.  If 
the  distinction  between  positive  and  negative  valence  is  recognized 
such  reactions  are  always  associated  with  changes  in  valence. 
According  to  this  conception  the  valence  of  any  uncombined 
element  is  always  zero,  that  of  any  combined  element  corresponds 
to  the  number  of  positive  or  negative  bonds  of  affinity  represented 
by  one  atom  of  the  element  in  the  compound  concerned.  For 
example,  the  valence  of  arsenic  is  sometimes  said  to  be  three  in 
both  arsine  and  arsenic  trioxide,  but  since  hydrogen  is  a  positive 
element  the  valence  of  arsenic  in  arsine  is  properly  represented  by 
-  3,  and  since  oxygen  is  a  negative  element  the  valence  of  arsenic 
in  arsenic  trioxide  is  properly  represented  by  +  3.  Hence  when 
arsine  is  oxidized  to  arsenic  trioxide  the  valence  of  the  arsenic 
changes  from  —  3  to  +  3. 

Definition  of  Oxidizing  Capacity.     In  many  of  the  substances 
used  as  oxidizing  agents  the  valence  of  only  one  of  the  atoms  in 

306 


PROCESSES  INVOLVING  OXIDATION  307 

the  molecule  changes;  in  such  cases  the  amount  of  oxidation 
which  can  be  effected  by  one  molecule  of  the  oxidizing  agent  is 
determined  by  the  change  in  the  valence  of  that  element.  In 
other  cases  two  or  more  atoms  change  their  valencies,  and  the 
amount  of  oxidation  which  can  be  effected  by  one  molecule  of  the 
oxidizing  agent  is  determined  by  the  algebraic  sum  of  the  valence 
changes  which  all  of  the  atoms  in  one  molecule  of  the  oxidizing 
agent  undergo.  The  " oxidizing  capacity"  of  any  agent  is  defined 
as  the  total  number  of  positive  valencies  furnished  to,  or  of  nega- 
tive valencies  taken  from,  the  substance  oxidized  by  one  molecule 
of  the  agent.  These  statements  can  be  illustrated  by  means  of  the 
following  reactions: 

(1)  CuS04+  Zn  ->  Cu  +  ZnS04, 

(2)  Fe(N03)3  +  Ag  ->  Fe(N03)2  +  AgN03, 

(3)  SnCl2  +  2  HgCl2  -»  SnCl4  +  2  HgCl, 

(4)  H2S  +  I2->S  +  2HI, 

(5)  3  H2S  +  8  HN03  ->  3  H2S04  +  8  NO  +  4  H20. 

In  (1)  the  valence  of  zinc  changes  from  0  to  +  2,  that  of  copper 
from  +  2  to  0.  The  oxidizing  capacity  of  copper  sulfate  is  here 
(+  2)  —  (0),  or  +  2.  The  oxidizing  capacity  of  zinc  is  (0)  —  (+2), 
or  —  2,  which  is  equivalent  to  saying  that  its  reducing  power  is  2. 

In  (2)  the  valence  of  silver  changes  from  0  to  +  1,  that  of  iron 
from  +  3  to  +  2.  The  oxidizing  capacity  of  ferric  nitrate  is  here 
(+  3)  _  (+  2),  or  +  1,  that  of  silver  is  (0)  -  (+  1),  or  -  1. 

In  (3)  the  valence  of  tin  changes  from  +  2  to  +  4,  that  of  mer- 
cury from  +  2  to  +  1.  The  oxidizing  capacity  of  stannous  chlo- 
ride is  (+  2)  -  (+  4),  or  -  2,  that  of  mercurous  chloride  is  (+  2) 
-  (+  1),  or  1. 

In  (4)  the  valence  of  sulfur  changes  from  -  2  to  0,  that  of 
iodine  from  -  0  to  —  1.  The  oxidizing  capacity  of  hydrogen 
sulfide  is  (-  2)  -  (0),  or  -  2,  that  of  iodine  is  (0)  -  (-  1),  or  1. 

In  (5)  the  valence  of  sulfur  changes  from  —  2  to  +  6,  that  of 


308  QUANTITATIVE  CHEMICAL  ANALYSIS 

nitrogen  from  +  5  to  +  2.  The  oxidizing  capacity  of  hydrogen 
sulfide  in  this  reaction  is  (-2)  -  (+6),  or  -  8,  that  of  nitric 
acid  is  (+  5)  -  (+  2),  or  +  3. 

Oxidation  and  lonization  Changes.  The  five  reactions  can 
also  be  expressed  in  terms  of  the  ionization  changes  concerned  as 
follows: 

(1)  Cu  +  S04  +  Zn-»  Cu  +  Zn  +  SO4, 

(2)  Fe++  3N03  +  Ag-»Fe  +  3N~03  +  Ag, 

(3)  Sn  +  6C1  +  2Hg-*+Sn++  6C1  +  2Hg, 

(4)  2H+~S~+_I2-*S 

(5)  " 


The  first  four  of  these  reactions  involve  changes  in  the  number 
of  charges  with  which  the  different  ions  are  associated  only,  and 
so  far  as  these  reagents  are  concerned  oxidation  can  be  defined  as 
any  process  in  which  the  number  of  positive  charges  associated 
with  an  element  is  increased,  or  the  number  of  negative  charges 
so  associated  is  decreased;  reduction  would  be  defined  by  the 
converse  statement.  Furthermore,  the  number  of  positive  charges 
gained  or  the  number  of  negative  charges  lost  is  a  measure  of  the 
oxidizing  capacity  of  the  reagent  concerned. 

In  the  fifth  reaction  there  is  also  a  change  in  the  composition  of 
one  of  the  ions,  that  is,  the  N03  ion  not  only  loses  its  negative 
charge  but  also  two  oxygen  atoms,  which  become  available  as 
oxidizing  agents.  Hence  this  method  of  defining  oxidation  and 
reduction,  which  in  many  respects  is  an  extremely  convenient  one 
to  use,  is  not  universally  applicable,  even  when  the  process  takes 
place  in  an  aqueous  solution. 

Normal  Values  of  Oxidizing  Agents.  The  oxidizing  capacity 
of  oxidizing  and  reducing  reagents  measures  one  of  the  forms  of 
chemical  activity  which  these  agents  exhibit.]  Since  the  unit  of 
oxidizing  capacity  which  has  been  adopted  is  the  change  in  valence, 


PROCESSES  INVOLVING  OXIDATION  309 

and  the  unit  of  valence  is  that  ordinarily  exhibited  by  the  hydro- 
gen atom,  the  oxidizing  capacity  of  a  reagent  is  identical  with  A 
of  the  general  formula,  and  the  normal  value  of  any  oxidizing  or 
reducing  agent  is  found  by  dividing  its  molecular  or  atomic  weight 
by  its  oxidizing  capacity. 

Meaning  of  Oxidation  Potential.  Altho  four  of  the  five  reac- 
tions cited  are  practically  irreversible,  reactions  (2)  and  many 
others  of  this  class  are  appreciably  reversible.  In  discussing 
the  reversibility  of  such  reactions  it  will  be  found  desirable  to 
conceive  of  every  oxidizing  and  reducing  agent  as  possessing  a 
definite  "  oxidation  potential,"  which  is  but  one  form  of  chemical 
potential,  and  to  ascribe  the  ability  of  one  reagent  to  oxidize 
another  to  the  fact  that  its  oxidizing  potential  is  large  as  com- 
pared with  that  of  the  reagent  oxidized.  Thus  the  negligible 
reversibility  of  reaction  (1)  would  be  ascribed  to  the  very  large 
oxidation  potential  of  copper  sulfate  as  compared  with  that  of 
metallic  zinc.  The  reversibility  of  (2)  would  be  ascribed  to  the 
fact  that  the  oxidizing  potential  of  ferric  nitrate  exceeds  that  of 
silver  by  a  small  amount  only.  The  comparative  values  of  the 
oxidizing  potentials  of  the  two  reagents  which  react  in  any  re- 
action involving  oxidation  is  shown  by  the  equilibrium  constants 
of  these  reactions.  The  equilibrium  constants  of  but  few  reactions 
of  this  type  have  been  determined  directly;  they  can  be  calcu- 
lated more  easily  in  many  cases  by  use  of  the  methods  of  electro- 
chemistry. 

Oxidation  and  the  Theory  of  the  Galvanic  Cell.  The  electro- 
motive force  produced  when  reactions  involving  oxidation  are 
made  to  take  place  in  such  a  manner  that  electrical  energy  instead 
of  heat  is  produced  is  found  to  be  directly  proportional  to  the 
equilibrium  constant  of  the  reaction.  If,  for  example,  reaction  (1) 
is  made  to  take  place  in  the  apparatus  represented  in  Fig.  59,  in 
which  A  represents  a  vessel  containing  a  bar  of  metallic  zinc  in 
contact  with  a  solution  of  zinc  sulfate,  and  B  a  vessel  containing  a 
bar  of  metallic  copper  in  contact  with  a  solution  of  copper  sulfate 


310 


QUANTITATIVE  CHEMICAL  ANALYSIS 


the  voltage  shown  by  the  voltmeter  V  measures  the  difference 
between  the  oxidizing  potentials  of  copper  sulfate  and  zinc.  The 
voltage  shown  by  such  cells  is  found  to  increase  with  an  increase 

in  the  concentration  of  the  copper  ion 
in  the  copper  solution  and  to  decrease 
with  the  concentration  of  the  zinc  ion 
in  the  zinc  solution,  and  a  formula, 
which  was  first  suggested  by  Nernst, 
makes  it  possible  to  calculate  at  what 
concentrations  all  action  would  cease, 
that  is,  the  concentrations  of  zinc  and 
copper  ions  in  a  solution  in  which  me- 
tallic zinc  and  copper  sulfate  would  be 

in  equilibrium.   The  ratio  of  these  con- 

++  ++ 

centrations,  that  is,  (Zn)  -r-  (Cu)  has 

been  found  to  have  the  value  1038.  In 
a  similar  manner  the  equilibrium  con- 
stant of  reaction  (2)  has  been  found 
to  have  the  value  0.1. 

Determination  of  Electrode  Poten- 
tials. The  electromotive  force  of  a 
galvanic  cell  is  determined  by  the  dif- 
ference between  the  electrode  poten- 
tials at  the  two  electrodes  of  which  the 
cell  is  composed.  The  difference  of 


Fig.  59.  —  Diagram  of  a 
Galvanic  Cell 


potential  at  each  electrode  is  determined  by  the  oxidizing  potential 
of  the  agent  which  undergoes  a  change  at  the  electrode.  Thus  the 
electrode  potential  of  copper  sulfate  in  contact  with  copper  de- 
pends upon  the  oxidizing  potential  of  the  copper  ion,  that  is, 
upon  the  ease  with  which  it  gives  up  its  positive  charges  to  some 
other  substance.  Hence  the  oxidizing  potentials  of  the  different 
oxidizing  agents  are  proportional  to  the  electrode  potentials  shown 
by  these  agents  when  they  undergo  a  reaction  in  a  galvanic  cell. 


PROCESSES  INVOLVING  OXIDATION  311 

If  a  numerical  value  is  arbitrarily  assigned  to  some  particular 
electrode  and  the  electromotive  force  of  the  cells  formed  by  com- 
bining this  electrode  with  a  number  of  other  electrodes  is  deter- 
mined; a  series  of  numbers  representing  the  comparative  values 
of  the  electrode  potentials  of  these  electrodes  can  be  calculated.  In 
attempting  to  prepare  electrodes,  whose  potential 
differences  shall  represent  the  oxidizing  potentials 
of  reagents  which  are  not  conductors  of  the  metallic 

class  and  which  do  not  yield  conductors  of  the    . 

metallic  class,  it  is  necessary  to  make  use  of  a  metal 
like  platinum  which  is  a  good  conductor  and  whose 
action  on  the  solution  is  so  small  that  it  can  be 
neglected.     Thus  in  measuring  the  oxidizing  poten- 
tial of  hydrogen  it  is  necessary  to  use  an  electrode 
which  measures  the  potential  difference  between 
gaseous  hydrogen  and  a  solution  of  the  hydrogen 
ion.     This  can  be  effected  by  use  of  the  device 
represented  in  Fig.  60.*     It  consists  of  a  sheet  of 
platinum  foil  bent  like  the  letter  S,  which  is  sur- 
rounded by  a  bell-shaped  glass  tube  of  such  a  form    ^ 
that  the  lower  half  of  the  foil  is  in  contact  with 
the  solution  and  the  upper  half  with  pure  gaseous     lg' 
hydrogen,  which  is  made  to  circulate  through  the 
apparatus  continuously.     The  potential  difference  shown  by  such 
an  electrode  also  depends  upon  the  oxidizing  potentials  of  such 
reagents  as  may  be  added  to  the  solution  in  contact  with  it,  and 
hence  it  can  be  used  to  measure  the  oxidizing  potentials  of  reagents 
like  ferric  salts  or  chromic  acid. 

A  Table  of  Electrode  Potentials.  In  the  table  which  appears 
below,  the  oxidizing  agents  whose  formulae  appear  in  the  first 
column  have  been  arranged  with  respect  to  the  numerical  value 
of  the  electrode  potential  to  which  they  give  rise  when  they  react 
in  a  galvanic  cell  in  the  manner  indicated  in  the  second  column. 
*  Hildebrand,  Jour,  of  Am.  Chem.  Soc.,  35,  847. 


312 


QUANTITATIVE  CHEMICAL  ANALYSIS 


TABLE  OF  ELECTRODE  POTENTIALS 


Oxidizing  agent 

Reaction  concerned 

Cone,  of  solution 

Electrode  potentials 

IVln04  —  ^  IVln 

<  +1.640 

dl 

C12^2C1 

(d)=i 

+1.640 

TT  P  O  -4-       *H 

Q~Q      >   Q 

<+1.270 

Br2 

Br2  -^  2  Br 

(Br)  =  l 

+1.270 

Ag 

Ag-»Ag 

(A+g)  =  l 

-f  +  +             +  + 

+1.076 

~Fe+ 

+Fe+-^  Fe 

(Fe)  =  (Fe) 

+1.016 

It 

I2-^2l 

_j  L. 

+0.80 

Cu 

Cu^Cu 

+0.606 

(H) 

(H)-»H 

+ 

+0.277 

(Pb) 

(Pb)  -»  Pb 

(Pb)  =  l 

+0.129 

(Cd) 

(Cd)  -»  Cd 

-H- 

(Cd)  =  l 

-0.143 

(Zn) 

(Zn)  ->  Zn 

(g)=i 

-0.493 

(Mg) 

(MJ20-»Mg 

(Mg)  =  l 

-1.273 

(Na) 

(Na)  -*  Na 

(Na)  =  l 

-2.483 

4- 

(Li) 

(Li)  ->  Li 

(Li)  =  l 

-2.744 

The  figures  given  in  the  last  column  represent  the  electrode  poten- 
tials when  the  concentration  of  the  solution  is  that  represented  in 
the  third  column.  In  general,  any  reagent  which  appears  in  the 
upper  part  of  the  table  should  oxidize  any  reagent  which  appears 
below  it,  that  is,  if  the  two  reagents  are  brought  together  the  one 
which  appears  first  in  the  table  reacts  in  the  manner  indicated  in 
the  second  column;  that  which  appears  later  reacts  in  the  reverse 
direction  of  that  indicated  in  the  second  column.  The  value  of 
the  equilibrium  constants  between  any  two  such  reagents  is  large 
in  proportion  as  the  difference  between  the  corresponding  electrode 
potentials  is  large.  Thus  the  very  large  equilibrium  constant  of 
reaction  (1)  accords  with  the  difference  between  the  electrode 


PROCESSES  INVOLVING  OXIDATION  313 

+  -H 

potentials  of  the  Cu  — »  Cu  and  the  Zn  — »  Zn  electrodes,  that  is, 
(+0.606)  -  (-493),  or  1.099  volts.  The  smaller  equilibrium  con- 
stant of  reaction  (2)  accords  with  the  smaller  difference  be- 
tween the  Ag  — >  Ag  and  the  Fe  — >  Fe  electrodes,  that  is,  (+1.076) 
-  (+1.016),  or  0.06  volt. 

The  Recognition  of  End-Points.  The  oxidizing  potentials  of 
mixtures  made  by  adding  together  equivalent  amounts  of  two 
reagents  which  react  completely  is  zero.  If  the  reaction  con- 
cerned was  not  absolutely  irreversible  such  mixtures  would  show 
a  slight  positive  or  negative  oxidation  potential  when  equivalent 
amounts  were  present.  It  is  possible  to  measure  the  electro- 
motive force  of  a  galvanic  cell,  one  electrode  of  which  consists  of 
a  hydrogen  electrode  placed  in  a  mixture  containing  equivalent 
proportions  of  two  oxidizing  agents,  with  great  accuracy.  If  such 
a  measurement  has  been  made,  the  true  end-points  of  titrations 
between  solutions  containing  these  reagents  can  be  ascertained 
by  carrying  the  titration  to  the  point  at  which  the  electromotive 
force  of  the  cell  corresponds  with  that  previously  found.  The 
electromotive  force  of  such  a  cell  also  changes  very  greatly  with 
very  slight  changes  in  the  ratio  between  the  quantities  of  the  two 
reagents  present  in  the  neighborhood  of  the  point  at  which  this 
ratio  is  one;  therefore  the  true  end-point  can  also  be  determined 
by  noting  the  rate  of  change  in  the  value  of  the  electromotive 
force  of  the  cell  during  the  titration. 

These  methods  of  determining  the  end-points  of  processes  of 
this  class  are  not  widely  used  at  present  altho  they  possess  decided 
advantages.  In  most  cases  the  end-point  is  determined  by  means 
of  an  indicator.  The  number  of  indicators  available  is  very 
limited  and  with  but  few  exceptions  they  can  only  be  used  for  one 
titration;  hence  their  action  will  be  considered  in  discussing  the 
particular  titration  in  which  they  are  used. 


CHAPTER  XLV 

DETERMINATIONS  WITH  POTASSIUM   PERMANGANATE 
I.  POTASSIUM  PERMANGANATE  AS  AN  OXIDIZING  AGENT 

Oxidizing  Potential  and  Oxidizing  Capacity.  This  is  a  par- 
ticularly useful  oxidizing  agent  since  solutions  of  it  act  completely 
and  instantaneously  with  a  large  number  of  reagents.  Its  oxi- 
dizing potential  has  not  been  measured  accurately,  but  exceeds 
that  of  all  the  reagents  listed  in  the  table  on  page  312. 

Its  reaction  with  a  ferrous  salt,  which  is  typical  of  a  large  num- 
ber of  oxidations  effected  by  it  in  an  acid  solution,  is  represented 
by  the  expression: 

(1)  2  KMn04  +  10  FeS04  +  8  H2S04  ->  5  Fe2(S04)3  +  2  MnS04 

+  K2S04  +  8H20. 

Assuming  that  the  degree  of  oxidation  of  the  potassium  has  a  con- 
stant value  of  +1,  and  that  of  sulfur  in  sulfates  is  —6  the  de- 
gree of  oxidation  of  the  manganese  changes  from  (2  X  4)  —  1,  or 
+  7,  to  (2X4)  —  6,  or  +  2,  and  hence  the  oxidizing  capacity  of 
one  molecule  of  the  permanganate  is  5.  Its  behavior  in  all  such 
reactions  may  also  be  represented  by  the  expression: 

(2)  2  KMn04  ->  K20  +  2  MnO  +  5  O. 

This  equation  represents  an  ideal  conception  only  and  will  not 
take  place  in  an  aqueous  solution  unless  some  acid  is  present,  which 
can  take  up  the  oxides  of  potassium  and  manganese,  and  some 
reducing  agent  is  present  to  take  up  the  available  oxygen. 

Its  use  in  a  neutral  solution  is  illustrated  by  its  reaction  with  a 
manganese  salt  according  to  the  expression: 

(3)  2  KMn04  +  3  MnCl2  +  2  H20  ->  5  MnO2  +  2  KC1  +  4  HC1. 

314 


DETERMINATIONS  WITH   POTASSIUM   PERMANGANATE       315 

In  this  reaction  the  degree  of  oxidation  of  the  manganese  changes 
from  (2  X  4)  -  1,  or  +  7,  to  (2  X  2),  or  +  4,  and  the  oxidizing 
capacity  of  one  molecule  of  the  permanganate  is  3.  Its  behavior 
in  reactions  of  this  type  is  therefore  correctly  represented  by  the 
expression: 

(4)  2  KMn04  ->  K20  +  2  Mn02  +  30. 

This  reaction  like  (2)  is  an  ideal  conception  and  does  not  take  place 
with  appreciable  velocity  unless  some  agent  which  is  capable  of 
utilizing  the  available  oxygen  is  present.  It  should  be  noted  that 
the  normal  value  of  potassium  permanganate  is  either  one-fifth  or 
one-third  of  its  molecular  weight  according  to  whether  it  is  used 
in  an  acid  or  in  a  neutral  solution. 

Factors  Which  Affect  Permanganate  Reactions.  When  this 
reagent  is  used  in  an  acid  solution  some  judgment  must  be  exer- 
cised with  respect  to  the  character  and  concentration  of  the  acid 
present.  Nitric  acid  is  usually  to  be  avoided,  since  it  is  itself  a 
strong  oxidizing  agent,  and  many  of  the  organic  acids  are  ob- 
jectionable since  some  of  them  reduce  potassium  permanganate. 
Hydrochloric  is  often  objectionable  owing  to  the  possibility  of  a 
reaction  taking  place,  which  is  represented  by  the  expression: 

(5)  2  KMn04  +  16  HC1  ->  2  KC1  +  2  MnCl2  +  5  C12  +  8  H20. 

In  the  presence  of  certain  metallic  ions,  especially  iron,  gold,  plati- 
num and  cadmium,  this  reaction  takes  place  even  in  moderately 
dilute  cold  solutions,  and  hence  erroneous  results  and  unsatisfac- 
tory end-points  are  obtained  in  the  titration  of  such  solutions. 
In  the  absence  of  these  ions  the  presence  of  moderate  concentra- 
tions of  hydrochloric  acid  is  not  objectionable.  Various  theories 
have  been  advanced  to  explain  this  phenomenon,  but  the  assump- 
tion that  the  ions  named  act  as  positive  catalyzers  is  as  satisfac- 
tory as  any.  The  effect  of  these  ions  is  largely  inhibited  by  the 
addition  of  large  amounts  of  a  manganous  salt,  that  is,  the  man- 
ganous  ion  seems  to  act  as  a  negative  catalyzer  for  reaction  (5). 
Altho  it  is  possible  to  counteract  the  effect  of  moderate  concen- 


316  QUANTITATIVE  CHEMICAL  ANALYSIS 

trations  of  hydrochloric  acid,  even  when  positive  catalyzers  are 
present,  by  the  addition  of  manganous  sulfate  the  conditions  which 
make  such  an  addition  necessary  should  be  avoided  whenever 

possible. 

In  view  of  the  above  statements  sulfuric  acid  is  usually  employed 
in  all  titrations  with  potassium  permanganate  which  are  effected 
in  an  acid  solution.  The  concentration  of  hydrogen  ion  neces- 
sary to  make  such  reactions  complete  and  instantaneous  varies. 
Reaction  (1)  is  found  to  be  sufficiently  complete  even  when  1  cc. 
of  concentrated  acid  per  100  of  solution  is  present;  that  is,  where 

(H)  =  0.35.     If  the  amount  of  acid  added  exceeds  40  cc.  per  100 
of  solution,  especially  if  the  temperature  is  much  above  20°  a 
further  secondary  reaction  becomes  possible  which  is  expressed  by 
the  equation 
(6)  2  KMn04  +  3  H2S04  -*  K2S04  +  2  MnS04  +  50. 

Determination  of  the  End-Point.  A  single  drop  of  a  one-tenth 
normal  solution  of  potassium  permanganate,  that  is,  one  contain- 
ing 3.16  gm.  per  liter  imparts  an  easily  recognizable  pink  color 
to  200  cc.  of  water.  Since  potassium  and  manganese  sulfates 
impart  no  color  to  aqueous  solutions  no  special  indicator  need  be 
used,  provided  the  compound  which  is  oxidized  yields  products 
whose  colorific  value  is  sufficiently  small.  Thus  the  true  end- 
point  of  reaction  (1)  can  be  easily  and  accurately  recognized,  since 
the  yellow  color  imparted  to  the  solution  by  the  small  concentra- 
tion of  ferric  ion  present  at  the  end-point  of  the  titration  is  negli- 
gible, as  compared  with  the  pink  color  produced  by  one  drop  of 
the  permanganate.  In  other  reactions,  such  as  the  reaction  by 
which  ferrocyanides  are  oxidized  to  ferricyanides,  the  red  color 
acquired  by  the  solution  before  the  end-point  is  reached  leads  to  a 
large  error. 

Possible  Uses.  The  more  important  determinations  which 
involve  the  use  of  a  standard  permanganate  solution  may  be  con- 
veniently classified  under  four  groups. 


DETERMINATIONS  WITH  POTASSIUM  PERMANGANATE       317 

First,  the  direct  oxidation  of  certain  metallic  elements  from  a 
lower  to  a  higher  degree  of  oxidation,  including,  in  addition  to  iron 
and  manganese,  the  elements  copper,  tin,  arsenic,  antimony,  tita- 
nium, molybdenum,  tungsten  and  uranium.  Some  of  these  processes 
are  unsatisfactory  or  are  less  convenient  than  other  methods. 

Second,  the  direct  oxidation  of  certain  inorganic  acids  or  their 
salts,  including  nitrous  acid,  which  is  oxidized  to  nitric;  sulfurous 
acid,  which  is  oxidized  to  sulfuric;  sulfhydric  acid,  which  is  oxi- 
dized to  sulfur  and  water;  ferrocyanic  acid,  which  is  oxidized  to 
ferricyanic  acid;  sulfocyanic  acid,  which  is  oxidized  to  hydro- 
cyanic and  sulfuric  acids,  and  hydrogen  peroxide  which  is  oxidized 
to  oxygen  and  water. 

Third,  the  direct  oxidation  of  certain  organic  substances  such 
as  oxalic  and  formic  acids,  and  tannin. 

Fourth,  a  large  number  of  indirect  determinations.  They  would 
include  elements  which  form  insoluble  compounds  with  the  acids 
enumerated  in  the  second  and  third  group,  and  which  can  there- 
fore be  separated  from  solution,  treated  with  a  stronger  acid  and 
the  liberated  acid  titrated.  Of  especial  interest  is  a  method  for 
the  determination  of  phosphorus  which  involves  precipitating  that 
element  as  ammonium  phosphomolybdate,  separating  from  the 
solution,  redissolving  and  reducing  the  molybdenum  in  the  solu- 
tion, and  titrating  the  latter. 

II.   PREPARATION  AND  STANDARDIZATION  OF  A  PER- 
MANGANATE SOLUTION 

Preparation.  Nearly  all  of  the  determinations  commonly 
made  with  potassium  permanganate  are  carried  out  in  an  acid 
solution.  A  solution  of  one-tenth  normal  strength,  assuming 
that  the  oxidizing  power  is  five,  is  usually  prepared;  it  should 
contain  3.16  gm.  per  liter.  If  it  becomes  desirable  to  use  such  a 
solution  for  determinations  which  are  carried  out  in  the  absence 
of  an  acid  it  should  be  remembered  that  it  is  only  0.06  normal  for 
all  such  determinations. 

/V/j^K-e  soTn       /0  «rr\  I  c.c  -        ,       /£,  ^  &  6  q  ^.,  /'/  *    •  ^7*  A/ 


318  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  potassium  permanganate  sold  by  dealers,  even  tho  marked 
C.  P.  usually  contains  small  amounts  of  manganese  dioxide;  further, 
when  dissolved  in  water  more  manganese  dioxide  slowly  separates 
owing  to  the  reducing  action  of  the  small  amount  of  organic  matter 
usually  present  even  in  distilled  water,  and  to  the  action  of  light. 
The  insoluble  dioxide  seems  to  catalyze  this  action  and  leads  to 
the  production  of  further  amounts  of  dioxide.  Hence  it  is  desir- 
able to  allow  the  prepared  solution  to  stand  for  twenty-four  hours, 
that  is,  until  the  easily  oxidizible  organic  matter  is  entirely  con- 
sumed, tnen  to  remove  the  dioxide  and  other  insoluble  impurities 
by  filtering  thru  asbestos,  and  to  preserve  the  solution  in  a  per- 
fectly clean  bottle  which  is  protected  from  strong  sunlight.  Under 
these  conditions  a  solution  can  be  preserved  for  many  months 
without  appreciable  reduction  in  strength. 

Methods  of  Standardization.  A  large  number  of  substances 
have  been  and  are  still  used  for  the  standardization  of  perman- 
ganate solutions.  Pure  metallic  iron,  which  has  been  deposited 
on  a  weighed  platinum  dish  by  means  of  an  electric  current,  has 
many  advantages,  but  since  this  deposit  contains  small  amounts  of 
carbon,  which  has  a  large  reducing  power,  the  results  are  slightly  in- 
accurate. Pure  ferrous  ammonium  sulfate,  FeSO^NKL^SO^O  H2O, 
is  still  more  convenient  but  the  purity  of  the  salt  sold  under  this 
name  cannot  be  assured,  and  it  is  necessary  to  test  each  sample 
for  its  reducing  power  by  some  independent  process.  Oxalic  acid 
is  sometimes  used,  but  unless  prepared  under  certain  definite 
conditions  its  purity  cannot  be  depended  upon. 

The  most  satisfactory  standard  is  sodium  oxalate,  which  can  be 
prepared  to  correspond  with  the  formula  Na2C20^under  conditions 
first  determined  by  Sorensen.*  The  proper  conditions  for  its  prep- 
aration, and  methods  of  ascertaining  its  purity  were  more  carefully 
elaborated  by  Blum,f  and  samples  of  guaranteed  purity  can  now 
be  purchased  from  the  Bureau  of  Standards  at  Washington. 

*  Zeit.  fur  analyt.  Chemie,  42,  512  (1903). 
t  Jour,  of  \m.  Chem.  Soc.  34,  123  (1912). 


DETERMINATIONS  WITH  POTASSIUM   PERMANGANATE       319 

Conditions  for  Titration  of  Sodium  Oxalate.  Oxalic  acid  can 
be  completely  oxidized  by  potassium  permanganate  according  to 
the  reaction: 

(7)        5  C2H204  +  2  KMn04  +  3  H2S04  ->  10  C02  +  K2S04 
+  2MnS04+8H20. 

At  ordinary  temperatures  the  velocity  of  this  reaction  is  very 
small,  but  at  60°  it  proceeds  almost  instantaneously,  and  after  the 
reaction  has  once  been  initiated  it  proceeds  fairly  rapidly,  even 
if  the  temperature  falls  below  60°.  The  concentration  ^  hydro- 
gen ion  necessary  to  make  the  reaction  complete  and  instanta- 
neous is  somewhat  greater  than  that  necessary  for  the  oxidation 
of  iron.  Either  sulfuric  or  hydrochloric  acid  can  be  used  to  sup- 
ply the  necessary  concentration  of  hydrogen  ion. 

Outline  of  Method  of  Procedure.  Weigh  out  6.32  of  pure  crys- 
tallized permanganate  into  a  400  cc.  beaker,  add  250  cc.  of  water, 
warm  slightly  and  stir  for  a  few  minutes,  then  pour  the  clear 
supernatant  liquid  into  a  2000  cc.  flask;  again  add  water,  warm, 
stir  and  pour  into  the  flask,  and  continue  this  cycle  of  operations 
until  all  of  the  salt  has  been  brought  into  solution.  Altho  the  salt 
is  highly  soluble  the  rate  of  solution  is  low  and  some  time  can  be 
saved  by  proceeding  as  directed.  Finally,  dilute  to  2000  cc.  and 
allow  to  stand  for  at  least  24  hours.  Prepare  an  asbestos  filter 
and  connect  with  a  clean  two-liter  bottle  as  shown  in  Fig.  58, 
then  filter  the  permanganate  solution  thru  it.  Keep  the  bottle 
in  a  dark  closet  or  cover  with  opaque  paper. 

Dry  some  pure  sodium  oxalate  (Sorensen)  for  a  half  hour  at  a 
temperature  of  250°.  Weigh  out  from  0.25  to  0.3  gm.  into  a 
400  cc.  beaker,  add  200  cc.  of  water,  then  slowly  add  5  cc.  of  con- 
centrated sulfuric  acid.  Heat  the  solution  to  80°  and  titrate 
slowly,  adding  the  permanganate  solution  until  a  faint  but  per- 
manent pink  color  appears. 

Divide  the  weight  of  sodium  oxalate  weighed  out  by  the  volume 
of  permanganate  solution  used  and  then  divide  the  quotient  by 


320  QUANTITATIVE  CHEMICAL  ANALYSIS 

the  weight  of  sodium  oxalate  present  in  a  normal  solution  of  that 
reagent  to  determine  the  relation  of  the  permanganate  solution 
to  normality.  Since  one  molecule  of  sodium  oxalate  yields  one  of 
oxalic  acid,  and  since  the  reducing  power  of  the  latter  is  two, 
1  cc.  of  normal  sodium  oxalate  should  contain  one  two-thousandth 
of  its  molecular  weight  expressed  in  grams. 

III.  DETERMINATION  OF  IRON  IN  CAST  IRON 

Interfering  Elements.  Cast  iron  usually  contains  several  per 
cent  oflBhcon  and  carbon  and  smaller  amounts  of  manganese,  sul- 
fur and  phosphorus.  If  dissolved  in  sulfuric  acid  the  silicon  forms 
silicic  acid,  the  manganese  forms  manganous  sulfate,  the  phos- 
phorus forms  phosphorous  acid  and  that  part  of  the  carbon  which 
exists  in  the  form  of  graphite  separates  as  such,  but  that  part 
which  exists  as  iron  carbide  (Fe3C)  yields  more  or  less  volatile 
hydrocarbons.  Even  if  the  resulting  solution  is  heated  to  boiling 
it  will  be  found  to  reduce  more  iron  than  would  correspond  to  the 
iron  present.  The  simplest  method  of  overcoming  this  difficulty 
is  to  destroy  these  reducing  substances  by  a  preliminary  treatment 
with  potassium  permanganate,  reduce  the  iron  necessarily  oxidized 
by  this  treatment  and  again  titrate  with  the  permanganate  solu- 
tion. If  a  slight  excess  of  permanganate  is  used  and  the  solution 
heated  during  the  preliminary  oxidation,  a  more  complete  oxida- 
tion of  these  reducing  substances  than  is  effected  in  the  final 
titration  can  be  assured,  and  experience  shows  that  the  products 
formed,  which  are  in  part  carbon  dioxide  and  water,  are  not 
reduced  by  the  method  used  for  the  reduction  of  the  iron. 

Methods  of  Reducing  Iron.  The  reducing  agents  employed 
for  this  purpose  must  be  slightly  soluble  solids  or  gases,  otherwise 
the  excess  necessarily  used  cannot  be  removed.  Of  the  possible 
solid  reagents,  metallic  zinc,  aluminum,  magnesium  and  lead  are 
most  frequently  used.  The  reactions  concerned  can  be  represented 
by  the  expression: 

(8)  Fe2(S04)3  +  Zn  ->  2  FeS04  +  ZnS04 


DETERMINATIONS  WITH   POTASSIUM   PERMANGANATE       321 


Reduction  with  these  reagents  is  always  effected  in  a  solution 
strongly  acidified  with  sulfuric  acid,  but  the  hydrogen  which  is 
also  produced  has  no  effect  on  the  degree  of  oxidation  of  the  iron, 
and  reduction  takes  place  only  at  the  surface 
of  the  metal  used.  Of  the  metals  named, 
aluminum  acts  somewhat  more  rapidly  than 
zinc  or  magnesium,  and  is  not  acted  upon  to 
the  same  extent  by  the  free  sulfuric  acid 
present ;  on  the  other  hand,  it  is  very  difficult 
to  obtain  the  metal  sufficiently  free  from  iron. 

Of  the  gaseous  reducing  agents,  hydrogen 
sulfide,  which  is  oxidized  by  ferric  iron  to 
sulfur  and  water,  and  sulfur  dioxide,  which 
is  oxidized  to  sulfuric  acid,  are  most  fre- 
quently used.  Both  reagents  reduce  the  iron 
rapidly  and  completely,  and  boiling  for  a  few 
minutes  expels  the  excess  used  completely. 
The  finely  divided  sulfur  which  is  formed 
when  the  former  reagent  is  used  is  without 
appreciable  action  on  the  permanganate  solu- 
tion unless  the  solution  is  hot.  When  sulfur 
dioxide  is  used  the  best  results  are  obtained 
when  the  solution  contains  a  very  slight 
excess  of  free  acid  only. 

Use  of  the  Jones  Reductor.  Since  reduc- 
tion takes  place  only  at  the  surface  of  the 
metal  used,  the  process  is  a  slow  one,  espe- 
cially if  the  solution  has  a  large  volume.  If, 
however,  the  metal  is  reduced  to  a  fine  state 


Fig.  61.  —  Jones  Re- 
ductor 


of  division  and  the  iron  solution  passed  slowly 
thru  a  tube  filled  with  it,  both  the  total  amount  of  metal  con- 
sumed and  the  time  required  for  complete  reduction  are  very 
greatly  reduced.  This  principal  is  made  use  of  in  the  Jones 
reductor  represented  in  Fig.  61.  Its  use  often  decreases  the  time 


322  QUANTITATIVE   CHEMICAL   ANALYSIS 

needed  for  complete  reduction  from  two  hours  to  fifteen  minutes. 
In  using  it  care  should  be  taken  to  prevent  air  from  coming  into 
contact  with  the  zinc  while  the  solution  is  being  reduced,  as  it  has 
been  shown  that  a  small  amount  of  hydrogen  peroxide,  which  is 
subsequently  oxidized  by  the  permanganate,  may  be  formed  under 
these  conditions. 

Outline  of  Method  of  Procedure.  Prepare  the  sample  either 
by  drilling  out  about  10  gm.  of  fine  powder,  or  by  turning  off  an 
equal'  amount  of  thin  shavings  from  the  metal  to  be  analyzed. 
Weigh  out  0.25  gm.  of  the  powdered  sample  into  a  200  cc.  beaker, 
add  25  cc.  of  dilute  sulfuric  acid,  warm  gently  and  allow  to  stand 
until  no  more  hydrogen  is  evolved,  and  only  gelatinous  silicic  acid 
and  graphite,  which  float  in  or  on  the  solution,  remain.  Add 
sufficient  permanganate  solution  to  impart  a  deep  red  color  to  the 
mixture,  even  after  it  has  been  warmed  to  50°.  Dissolve  the 
precipitate  of  manganese  dioxide,  which  usually  separates,  by 
the  careful  addition  of  a  few  crystals  of  sodium  sulfite,  but  avoid 
using  more  than  is  absolutely  necessary.  Filter  the  mixture,  using 
a  9  cm.  filter  and  washing  the  latter  free  from  iron,  but  endeavor 
to  keep  the  total  volume  less  than  100  cc. 

Prepare  a  Jones  redactor  as  follows:  Dissolve  5  gm.  of  metallic 
mercury  in  50  cc.  of  dilute  nitric  acid  and  dilute  the  solution  to  250 
cc.  Add  250  gm.  of  granulated  zinc,  which  is  fine  enough  to  pass 
a  20-  but  not  fine  enough  to  pass  a  30-mesh  sieve.  Stir  the  mix- 
ture for  a  few  minutes,  then  pour  off  the  solution  and  wash  the 
residual  metal  until  free  from  nitric  acid  and  nitrates.  Place  a 
disk  of  perforated  platinum  foil  in  the  bottom  of  the  reductor  tube, 
cover  this  with  a  thin  layer  of  glass  wool  and  finally  fill  with  the 
amalgamated  zinc  as  far  as  the  cuplike  enlargement  at  the  top. 
Connect  the  tube  with  the  flask  and  the  latter  with  a  suction  pump. 
Rinse  out  the  tube  by  passing  thru  it  250  cc.  of  dilute  sulfuric 
acid  (5  of  cone,  acid  to  100  of  water)  being  careful  never  to  let  the 
liquid  get  below  the  top  of  the  zinc  column. 

Next  pass  the  iron  solution  thru  the  reductor,  regulating  the 


DETERMINATIONS  WITH   POTASSIUM   PERMANGANATE       323 

pump  so  as  to  require  about  fifteen  minutes  for  the  passage  of 
the  entire  solution,  and  as  soon  as  the  latter  reaches  the  top  of 
the  zinc  column  rinse  out  by  the  use  of  200  cc.  of  dilute  sulfuric 
acid. 

Remove  the  flask  from  the  reductor  tube  and  titrate  the  solution 
without  delay.  Calculate  the  percentage  of  iron  present  in  the 
solution,  noting  that  since  its  degree  of  oxidation  is  increased  from 
two  to  three  its  reducing  power  is  one. 

IV.   DETERMINATION  OF  POTASSIUM  NITRITE  IN  THE  COM- 
MERCIAL SALT 

Theory  of  the  Method.  The  action  of  potassium  permanga- 
nate on  nitrous  acid  is  represented  by  the  expression: 

(9)        5  HN02  +  2  KMn04  +  3  H2S04  ->  5  HN03  +  K2S04 
+  2  MnS04  +  3  H20. 

When  nitrous  acid  is  titrated  with  potassium  permanganate  in 
a  dilute  solution  the  reaction  is  complete  and  instantaneous  as 
long  as  either  reagent  is  present  in  moderately  large  excess,  but 
as  the  end-point  is  approached  the  rate  of  action  becomes  extremely 
slow,  and  it  is  not  possible  to  determine  the  correct  end-point  with 
even  approximate  accuracy.  If,  however,  an  excess  of  perman- 
ganate is  added  to  the  nitrous  acid  solution  the  latter  is  rapidly 
and  completely  oxidized,  and  the  excess  of  permanganate  used 
can  be  determined  by  titrating  with  a  standard  solution  of  a 
ferrous  salt,  or  by  adding  an  excess  of  a  ferrous  salt  and  titrating 
back  with  the  permanganate;  there  is  little  danger  that  reaction 
(9)  will  reverse,  that  is,  that  nitric  acid  will  be  reduced  to  nitrous 
acid  by  either  the  ferrous  or  manganous  salt  present,  provided  the 
solution  is  cold  and  dilute. 

Potassium  nitrite  is  decidedly  hygroscopic  and  an  average 
sample  cannot  be  obtained  unless  it  is  thoroughly  mixed  and  unless 
several  grams  are  weighed  out.  It  does  not  ordinarily  contain 
any  other  substances  which  interfere  with  the  titration. 


. 

324  QUANTITATIVE   CHEMICAL  ANALYSIS 

Outline  of  Method  of  Procedure.  Prepare  a  solution  of  ferrous 
sulfate  by  dissolving  28  gm.  of  the  crystallized  salt  (FeSO4-7  H20) 

/    in  water,  adding  10  cc.  of  concentrated  sulfuric  acid  and  diluting 
to  one  liter.     Determine  the  volumetric  relation  between  this  and 

/    the  permanganate  solution  by  titrating  25  cc. 

'"Weigh  out  4  gm.  of  the  well-mixed  sample  in  a  weighing  bottle, 
dissolve  and  dilute  to  500  cc.  in  a  graduated  flask  and  mix  thor- 
oughly. Remove  25  cc.  of  this  solution  to  a  250  cc.  beaker  or 
Erlenmeyer  flask,  add  exactly  50  cc.  of  the  permanganate  solution 
and  allow  to  stand  for  a  few  minutes.  Next  add  5  cc.  of  dilute 
sulfuric  acid  and  shake  or  stir  for  a  few  minutes,  then  add  25  cc. 
of  the  ferrous  sulfate  solution  and  finally  titrate  with  the  perman- 
ganate solution.  Calculate  the  volume  of  permanganate  solution 
which  would  be  equivalent  to  the  25  cc.  of  ferrous  sulfate  solution 
used  and  subtract  from  the  total  volume  of  permanganate  em- 
ployed. Calculate  the  weight  of  KN02  corresponding  to  this 
volume  of  permanganate  assuming  that  the  reducing  power  of  the 
KN02  is  two.  Report  the  per  cent  present  in  the  sample. 

(JQ/ 

V.  DETERMINATION  OF  CALCIUM  IN  LIMESTONE 

Theory  of  the  Method.  The  insolubility  of  calcium  oxalate 
and  the  ease  with  which  oxalic  acid  can  be  titrated  with  potassium 
permanganate  forms  the  basis  of  an  exceedingly  useful  indirect 
method  for  the  determination  of  this  element.  The  accuracy  of 
the  method  depends,  first,  upon  the  completeness  with  which  the 
oxalate  can  be  separated  from  the  solution  and  from  any  other 
oxalates  which  may  be  occluded  or  co-precipitated  with  it;  second, 
upon  the  equilibrium  constant  of  the  reaction: 

(10)  CaC204  +  H2S04  ->  CaS04  +  H2C204, 

and  third  upon  the  equilibrium  constant  of  reaction  (7)..  The 
first  of  these  factors  is  discussed  in  Chapter  XXIV  and  it  is  there 
show*  that  even  in  the  presence  of  magnesium  the  error  involved 
in  the  separation  can  be  made  very  small.  The  constant  for 


DETERMINATIONS  WITH  POTASSIUM  PERMANGANATE       325 

reaction  (10)  is  large  since  the  dissociation  constant  of  oxalic  acid 
is  much  smaller  than  that  of  sulfuric  acid.  The  constant  for 
reaction  (?Xas  shown  in  an  earlier  paragraph  of;  this  chapter )is  also 
very  large. 

Outline  of  Method  of  Procedure.  Weigh  out  0.5  gm.  of  the 
sample  into  a  100  cc.  beaker,  cover  with  a  watch  glass  and  intro- 
duce 10  cc.  of  dilute  hydrochloric  and  5  of  dilute  nitric  acid,  and 
warm  on  a  sand  or  steam  bath  until  the  decomposition  seems  to  be 
complete,  and  fumes  of  NO  and  Cl  are  no  longer  given  off.  Rinse 
off  and  remove  the  watch-glass  cover  and  bring  the  volumes  of  the 
solution  to  100  cc. 

Heat  the  solution  nearly  to  boiling,  add  a  slight  excess  of  am- 
monium hydroxide,  digest  for  a  few  minutes,  then  filter  on  a  9  cm. 
filter  and  wash  until  free  from  soluble  salts.  If  the  volume  of 
iron  and  aluminum  hydroxide  thus  obtained  is  large,  redissolve 
and  precipitate  and  combine  the  two  filtrates. 

Dilute  the  filtrate  to  300  cc.,  add  a  drop  of  methyl  orange 
indicator  and  dilute  hydrochloric  acid  until  the  solution  gives  a 
neutral  reaction.  Heat  to  boiling,  add  25  cc.  of  oxalic  acid  solu- 
tion and  stir  for  a  few  minutes;  if  a  precipitate  does  not  separate 
add  a  single  drop  of  ammonium  hydroxide  and  stir  rapidly.  After 
about  ten  minutes  add  diluted  (1:4)  ammonium  hydroxide  slowly 
and  with  constant  stirring  until  the  solution  is  distinctly  alkaline; 
finally  allow  the  mixture  to  stand  for  at  least  an  hour. 

Filter  off  the  precipitate  on  a  9  cm.  filter  and  wash  both  precip- 
itate and  filter  very  thoroughly,  that  is,  until  the  washings  show 
no  action  on  a  drop  of  permanganate  solution  even  after  acidifying 
and  heating  to  80°. 

Remove  the  filter  from  the  funnel,  open  it  out  and  flatten  against 
the  side  of  a  400  cm.  beaker.  Rinse  the  precipitate  adhering  to 
the  filter  into  the  bottom  of  the  beaker  and  bring  the  total  volume 
up  to  200  cc.  Add  5  cc.  of  concentrated  sulfuric  acid,  heat  to  80° 
and  titrate  with  the  permanganate  as  in  the  standardization. 

Calculate  and  report  the  percentage  of  CaO  present^  noting  that 


326  QUANTITATIVE  CHEMICAL  ANALYSIS 

since  one  atom  of  calcium  precipitates  one  molecule  of  calcium 
oxalate  and  the  latter  yields  one  molecule  of  oxalic  acid,  which  has 
a  reducing  power  of  two,  the  correct  per  cent  is  given  by  the 
formula: 

Mol.wt.CaO  X  N  X  VQl'  f  Mn°14  X  100  =  per  cent  CaO, 
2  X  1000  wt.  of  sample 

in  which  N  represents  the  normality  of  the  solution  used. 


VI.  QUESTIONS  AND  PROBLEMS:  -  SERiES-22 

1.  Outline  the  method  of  reasoning  by  which  you  decide  upon  the  reduc- 
ing capacity  of  the  two  metallic  elements  and  the  two  acids  oxidized  by 
potassium  permanganate  according  to  the  equations  given  below : 

2  KMnO4  4-  5  Ti2(SO4)3  +  8  H2SO4  ->  10  Ti(S04)2  +  K2S04  +  2  MnSO4 

+  8H20, 
?        2  KMn04  +  5  U (SO4)2  +  2  H2O  ->  5  (UO)2S04  +  K2SO4  +  2  MnSO4 

+  2H2SO4,  dtiify'-0* 

14  KMnO4  +  Mo24O37  +  21 H2SO4  ->  24  MoO3  +  14  MnSO4  +  7  K2SO4 

+  21  H2O, 

12  KMnO4  -f  10  HCNS  +  8  H2SO4  -»  10  HCN  +  6  K2SO4  +  12  MnSO4 
+  8H2O. 

2.  Write  out  the  reactions  in  which  potassium  permanganate'  oxidizes  tin 
from  the  divalent  to  the  quadrivalent  condition,  and  arsenic  and  antimony 
from  the  trivalent  to  the  quinquivalent  condition  in  acid  solutions. 

3.  When  water  acts  on  calcium  carbide  C2H2  is  produced,  when  it  acts 
on  aluminum  carbide  CH4  is  produced,  what  are  the  probable  formulae  of 
the  two  carbides? 

4.  What  weight  of  phosphorus  would  be  represented  by  one  cc.  of  a  one- 
tenth  normal  solution  of  potassium  permanganate  assuming  that  the  phos- 
phorus was  precipitated  as  (NH4)3PO4-12  MoO3,  the  precipitate  dissolved  and 
reduced  to  Mo24O3;,  and  the  latter  titrated  by  the  reaction  given  in  the  first 
problem? 

5.  What  weight  of  copper  would  be  represented  by  one  cc.  of  a  one-tenth 
normal  solution  of  potassium  permanganate,  assuming  that  the  copper  was 
precipitated  as  CuCNS  and  the  precipitate  oxidized  to  CuSO4,  HCN  and 
H2SO4  by  the  permanganate  solution? 


DETERMINATIONS  WITH   POTASSIUM   PERMANGANATE       327 

6.  What  weight  of  potassium  permanganate  should  be  present  in  one  cc. 
of  the  solution  in  order  that  each  cc.  should  represent  three  milligrams  of 
manganese  if  precipitated  by  reaction  (3)? 

7.  How  much  antimony  would  be  represented  by  one  cc.   of  a  solution 
containing  3  gm.  of  KMnO4  per  liter,  assuming  that  the  antimony  is  pre- 
cipitated as  sulfide,  the  sulfide  added  to  a  solution  of  ferric  sulfate  and  the 
reduced  iron  titrated  according  to  the  reactions: 

5  Fe2(SO4)3  +  Sb2S3  +  6  H2O  -»  2  HSbO3  +  3  S  +  10  FeSO4  +  5  H2SO4, 
2  KMnO4  +  10  FeSO4  +  8  H2SO4  -»  5  Fe2(SO4)3  +  K2SO4  +  2  MnSO4 
+  8H2O 

8.  In  determining  iron  in  a  sample  of  cast  iron  which  contained  95  per  cent 
of  iron  and  3  per  cent  of  carbon,  one-tenth  of  the  latter  remains  in  solution  as 
C2H2  and  is  oxidized  to  carbon  dioxide  and  water  by  the  permanganate,  what 
is  the  error  in  the  determination  of  iron? 

9.  Suggest  indirect  methods  for  the  determination  of  the  elements  arsenic, 
cobalt  and  zinc  in  which  potassium  permanganate  is  used  as  the  oxidizing 
agent. 


CHAPTER  XLVI 

DETERMINATIONS  WITH  POTASSIUM   BICHROMATE 
I.  POTASSIUM  BICHROMATE  AS  AN  OXIDIZING  AGENT 

Oxidizing  Potential.  This  reagent  is  used  as  an  oxidizing 
agent  in  an  acid  solution,  and  altho  in  its  general  behavior  it 
resembles  potassium  permanganate  the  data  given  in  the  table 
on  page  312  shows  that  its  oxidizing  potential  is  somewhat  less. 
The  salts  of  certain  metals  which  are  completely  oxidized  from  a 
lower  to  a  higher  degree  of  oxidation  by  the  permanganate  are 
only  partially  oxidized  by  the  dichromate;  further,  the  dichromate 
has  but  little  action  upon  oxalic  and  other  organic  acids  unless  the 
solutions  used  are  hot  and  concentrated.  Its  solutions  are  so 
stable  that  they  can  be  preserved  for  months  without  loss  of 
strength,  even  when  exposed  to  strong  sunlight. 

Oxidizing  Capacity.  The  oxidizing  capacity  of  this  reagent  is 
best  shown  in  the  reaction  which  takes  place  when  it  is  brought 
into  contact  with  a  ferrous  salt,  and  which  can  be  expressed  as 
follows: 

(1)  K2Cr207  +  6  FeCl2  +  14  HC1  ->  6  FeCl3  +  2  KC1  +  2  CrCl3 

+  7H20 

Since  this  reaction  involves  the  reduction  of  the  chromium  from 
chromium  trioxide,  whose  degree  of  oxidation  is  represented  by 
+  6,  to  a  salt  of  chromium,  in  which  the  degree  of  oxidation  is 
represented  by  +  3,  the  oxidizing  power  of  one  molecule  of  the 
dichromate,  which  can  be  regarded  as  a  combination  of  one  mole- 
cule of  potassium  oxide  with  two  of  chromium  trioxide,  is  two 
times  the  difference  between  six  and  three  or  six.  The  decomposi- 
tion of  the  dichromate  may  also  be  represented  by  the  equation: 

(2)  K2Cr207  -+  K20  +  Cr203  +  30. 

328 


DETERMINATIONS  WITH  POTASSIUM   BICHROMATE       329 

The  latter,  like  the  corresponding  equation  for  the  permanga- 
nate, is  an  ideal  conception  only,  and  does  not  take  place  in  solution 
unless  it  contains  a  sufficient  amount  of  acid  to  take  up  the  oxides 
of  potassium  and  chromium,  and  a  reducing  agent  of  sufficient 
strength  to  utilize  the  available  oxygen. 

Conditions  Necessary  for  the  Titration.  Reaction  (1)  is  both 
complete  and  instantaneous  if  a  concentration  of  hydrogen  ion 
corresponding  to  that  represented  by  about  1  cc.  of  the  concen- 
trated hydrochloric  acid  per  100  of  solution  is  present.  There  is 
but  little  danger  of  interaction  with  the  acid  itself  and  consequent 
liberation  of  chlorine,  unless  the  solution  is  hot,  or  unless  the 
concentration  of  acid  exceeds  forty  times  the  minimum  value 
named.  Sulfuric  and  acetic  acids,  if  added  in  amounts  sufficient 
to  yield  concentrations  of  hydrogen  ion  equal  to  that  resulting 
from  the  minimum  concentration  of  hydrochloric  acid  named, 
can  also  be  used  to  acidify  the  solution. 

Determination  of  the  End-Point.  The  intensity  of  the  yellow 
color  of  solutions  containing  Cr207  ions  is  much  less  than  the  red 
color  of  those  containing  corresponding  concentrations  of  sMn04 

ions,  and  furthermore  the  Cr  ions  formed  when  Cr207  or  Cr04 
are  reduced,  impart  a  very  intense  green  color  to  the  solution. 

In  the  titration  of  iron  salts  the  end-point  can  be  determined 
by  the  use  of  a  test  which  distinguishes  between  ferrous  and  ferric 
ions;  in  the  titration  of  other  reducing  agents  it  becomes  necessary 
to  add  an  excess  of  the  dichromate  solution,  and  to  determine 
the  amount  added  in  excess  by  titrating  back  with  a  standard 
solution  of  a  ferrous  salt. 

Potassium  f erricyanide  reacts  with  a  ferrous  salt  as  follows : 

(3)          2  K3Fe(CN)6  +  3  FeCl2  ->  Fe3[Fe(CN)6]2  +  6  KC1. 

The  ferrous  ferricyanide  produced  is  insoluble  even  in  acid  solu- 
tions, and  has  a  very  intense  blue  color.  It  is  possible  to  recognize 
by  this  test  one  part  of  ferrous  ion  in  one  hundred  thousand  of 
water.  Ferric  salts  do  not  react  with  the  reagent,  but  when  the 


330  QUANTITATIVE   CHEMICAL  ANALYSIS 

concentration  of  the  ferric  ions  is  sufficiently  large  and  that  of  the 
ferrous  ions  small,  the  yellow  color  of  the  ferric  ion  masks  the  blue 
coloration  normally  produced  by  the  indicator  and  gives  a  green 
coloration. 

If  the  indicator  is  added  directly  to  the  solution  in  which  the 
titration  is  being  made  the  ferrous  ferricyanide  precipitate  pro- 
duced remains  unaffected,  even  after  an  excess  of  potassium  di- 
chromate  has  been  added.  It  becomes  necessary,  'therefore,  to 
use  this  reagent  as  an  "  outside  indicator/7  that  is,  to  remove  and 
test  a  drop  of  the  solution  from  time  to  time  during  the  titration. 
These  tests  will  first  yield  a  deep  blue  precipitate;  slightly  before 
the  true  end-point  is  reached  they  will  show  a  green  coloration; 
at  the  true  end-point  a  clear  yellow;  and  when  an  excess  of  di- 
chromate  is  present  a  slight  brown. 

The  accuracy  of  this  method  of  determining  the  end-point  is 
affected  by  a  number  of  details.  If  the  indicator  solution  used 
has  stood  for  more  than  twenty-four  hours  in  strong  sunlight  it 
will  be  found  to  contain  some  ferrocyanide  and  hence  will  give 
misleading  results.  If  its  concentration  exceeds  one-fifth  of  one 
per  cent,  the  end-points  are  not  clearly  defined.  Further,  the  size 
of  the  drop  of  indicator  solution  used,  as  compared  with  the  size 
and  concentration  of  the  drop  of  solution  which  is  tested  affect  the 
final  color.  Even  those  tests  which  show  no  reaction  for  ferrous 
iron  at  first,  gradually  develop  a  blue  color,  owing  to  the  gradual 
reduction  of  some  of  the  iron  by  the  light,  and  hence  a  definite 
time  interval  should  be  observed  in  judging  whether  the  true  end- 
point  has  been  reached. 

Special  Advantages  of  Potassium  Bichromate.  This  reagent 
does  not  oxidize  hydrochloric  acid,  even  in  the  presence  of  iron 
salts,  and  hence  it  can  often  be  used  when  potassium  perman- 
ganate cannot  be  employed.  Since  most  of  the  ores  of  iron  can- 
not be  brought  into  solution  without  the  use  of  hydrochloric  acid, 
and  since  the  iron  in  such  ores  can  be  reduced  more  rapidly  by  the 
use  of  stannous  chloride  than  by  any  other  method,  the  process  is 


DETERMINATIONS  WITH   POTASSIUM   BICHROMATE       331 

peculiarly  adapted  to  the  determination  of  iron  in  iron  ores.  Altho 
it  oxidizes  a  number  of  other  metals  by  reactions  which  are  both 
complete  and  instantaneous  it  is  rarely  used  for  the  determina- 
tion of  such  metals,  owing  to  the  difficulty  of  ascertaining  the 
end-point  of  these  reactions. 

II.   PREPARATION  AND  STANDARDIZATION  OF  A  DICHROMATE 

SOLUTION 

Method.  The  potassium  dichromate  sold  by  dealers  often 
contains  small  amounts  of  potassium  sulfate,  but  can  be  easily 
purified  by  recrystallization.  Since  the  salt  is  not  appreciably 
hygroscopic  an  accurately  standardized  solution  can  be  prepared 
by  weighing  out  a  definite  amount,  dissolving,  and  diluting  to  the 
proper  volume.  As  the  solution  is  most  frequently  used  for  the 
determination  of  iron  it  is  convenient  to  prepare  it  according  to 
the  unitary  system,  that  is,  so  that  1  cc.  will  oxidize  exactly  0.005 
gm.  of  Fe.  As  already  noted  there  are  a  number  of  factors  which 
affect  the  method  used  to  determine  the  end-point  of  the  reaction, 
and  it  is  always  advisable  to  check  the  theoretical  value  of  the 
solution  by  titrating  it  against  a  known  weight  of  a  pure  ferrous 
ammonium  sulfate  under  definite  conditions. 

Detailed  Outline  of  Method.  Weigh  out  exactly  4.39  gm.  of 
the  pure  salt,  dissolve  in  water  and  dilute  to  exactly  one  liter. 
Weigh  out  1  gm.  of  pure  ferrous  ammonium  sulfate,  dissolve  in 
100  cc.  of  water,  add  5  cc.  of  concentrated  hydrochloric  acid  and 
titrate  with  the  dichromate  solution.  Use  as  an  indicator  a 
freshly  prepared  solution  of  potassium  ferricyanide  made  by  dis- 
solving a  crystal  of  the  pure  salt  as  large  as  a  grain  of  wheat  in 
25  cc.  of  water.  Add  at  once  to  the  iron  solution  26  cc.  of  the  di- 
chromate solution,  and  then  test  the  mixture  for  unoxidized  iron 
by  bringing  a  drop  of  it  into  contact  with  a  drop  of  the  indicator 
on  a  porcelain  plate,  or  piece  of  glazed  white  paper.  If  the  test 
shows  an  intense  blue  color  continue  adding  the  dichromate  solu- 
tion in  quantities  of  two-tenths  of  a  cubic  centimeter  at  a  time 


332  QUANTITATIVE  CHEMICAL  ANALYSIS 

until  the  test  shows  a  light  blue  only,  then  continue  adding  in 
quantities  of  two  drops  at  a  time  until,  after  passing  thru  various 
shades  of  blue  and  green,  the  tests  show  a  clear  yellow  only  which 
persists  for  at  least  two  minutes.  Calculate  the  weight  of  iron 
actually  oxidized  by  1  cc.  of  the  solution. 

III.  DETERMINATION  OF  IRON  IN  IRON  ORES 

Decomposition.  The  more  easily  soluble  ores  of  iron,  includ- 
ing siderites,  which  are  mainly  ferrous  carbonate,  and  many  of  the 
hematites  and  magnetites,  which  are  mainly  ferric  oxide  and  fer- 
rous-ferric oxide  respectively,  are  dissolved  by  treatment  with 
warm  concentrated  hydrochloric  acid.  The  action  of  this  acid  is 
greatly  intensified  by  the  addition  of  a  small  amount  of  stannous 
chloride.  A  small  amount  of  insoluble  residue  resulting  from 
treatment  with  these  reagents  is  usually  assumed  to  be  free  from 
iron  and  disregarded,  provided  it  is  of  a  pure  white  color;  it  may 
contain  small  amounts  of  iron  in  the  form  of  an  insoluble  silicate. 
Many  samples  of  limonite  ores,  which  contain  carbonates  and 
sometimes  organic  matter,  and  many  ores  which  contain  sulfur, 
yield  to  the  hydrochloric  acid  and  stannous  chloride,  only  after 
ignition  in  an  open  crucible;  this  treatment  also  oxidizes  the 
organic  matter,  the  presence  of  which  might  lead  to  high  results. 

The  more  difficultly  soluble  ores,  including  many  varieties  of 
hematite,  magnetite  and  limonite  and  all  ores  containing  iron  in 
the  form  of  an  insoluble  silicate,  are  most  easily  and  completely 
decomposed  by  fusion  with  sodium  peroxide.  This  treatment 
yields  ferrates  and  silicates  of  sodium,  also  aluminates,  chromates 
and  manganates  if  these  elements  are  present,  all  of  which  com- 
pounds are  easily  decomposed  by  hydrochloric  acid.  The  excess 
of  sodium  peroxide  used,  also  the  chromates  and  manganates,  are 
completely  reduced  by  heating  with  hydrochloric  acid  and  any 
chlorine  which  may  be  liberated  is  either  volatilized  or  is  reduced 
by  the  stannous  chloride  used  to  reduce  the  iron. 

The  action  of  the  molten  peroxide  of  sodium  on  platinum  cru- 


DETERMINATIONS  WITH   POTASSIUM   BICHROMATE       333 

cibles  is  sufficiently  energetic  to  render  their  use  unadvisable;  its 
action  on  nickel  is  also  appreciable  and  both  nickel  and  iron,  small 
amounts  of  which  are  usually  present  in  the  metal  of  which  such 
crucibles  are  made,  are  usually  introduced  into  the  resulting  solu- 
tion in  sufficient  amounts  to  produce  appreciable  errors.  Crucibles 
of  silver  may  be  used  to  advantage  but  well-glazed  porcelain  ones 
answer  very  well,  for  although  the  glaze  is  gradually  disintegrated 
no  error  is  introduced  as  it  does  not  contain  iron,  and  the  crucible 
can  usually  be  employed  for  several  analyses. 

Reduction  of  Iron  by  Means  of  Stannous  Chloride.  Ferrous 
salts  can  be  reduced  by  stannous  salts  as  represented  by  the 
equation 

(4)  SnCl2  +  2  FeCl3  ->  SnCl4  +  2  FeCl2. 

This  reaction  is  almost  complete  and  instantaneous  provided 
the  solutions  concerned  are  hot  and  concentrated,  and  provided  a 
rather  large  concentration  of  hydrochloric  acid  is  also  present. 
Since  solutions  of  ferric  salts,  especially  when  hot  and  when  Cl 
ions  are  present,  possess  an  intense  red  or  yellow  color,  whereas 
solutions  of  ferrous  salts  show  a  slight  greenish  color  only,  the 
point  at  which  sufficient  stannous  chloride  has  been  added  to  com- 
pletely reduce  the  iron  in  a  solution  can  be  determined  with  suffi- 
cient accuracy  by  noting  the  color  changes  of  the  solution. 

It  is  scarcely  possible  to  reduce  all  of  the  iron  in  a  solution  with- 
out introducing  a  slight  excess  of  stannous  chloride  and  since  the 
latter  reduces  chromic  acid,  this  excess  must  be  oxidized  before 
tit  ration,  without  at  the  same  time  reoxidizing  any  of  the  iron. 
This  can  be  effected  by  means  of  mercuric  chloride  which  easily 
oxidizes  the  tin  but  not  the  iron,  and  is  itself  reduced  to  insoluble 
mercurous  chloride,  which  compound  is  not  affected  by  chromic 
acid.  If,  however,  the  solution  is  hot,  and  if  its  concentration 
with  respect  to  stannous  chloride  is  large  as  compared  with  that 
of  the  mercuric  chloride  the  reduction  may  go  farther  and  metallic 
mercury  may  be  formed,  which  unlike  mercurous  chloride  is 


334  QUANTITATIVE  CHEMICAL   ANALYSIS 

capable  of  reducing  chromic  acid.  For  this  reason  care  must  be 
taken  in  using  this  process  to  add  a  slight  excess  of  stannous 
chloride  only,  to  cool  or  dilute  before  adding  the  mercuric  chloride, 
and  to  add  a  relatively  large  amount  of  the  latter. 

Effect  of  Other  Elements  on  the  Process.  This  method  is  not 
affected  by  the  presence  of  even  large  amounts  of  aluminum, 
manganese,  zinc,  cadmium,  calcium  or  magnesium.  Cobalt  and 
nickel  in  small  amounts  are  not  objectionable,  but  large  amounts 
affect  the  accuracy  of  the  end-point.  Chromium,  in  large  amounts, 
increases  the  difficulty  of  recognizing  the  point  at  which  the  proper 
excess  of  stannous  chloride  has  been  added,  but  in  small  amounts 
is  not  objectionable.  Copper,  since  it  is  reduced  to  the  cuprous 
form  by  stannous  chloride  and  reoxidized  to  the  cupric  form  by 
the  dichromate,  increases  the  amount  of  standard  solution  used 
almost  in  proportion  to  the  amount  present  and  also  masks  the 
end-point.  Antimony  and  titanium  are  also  reduced  by  stannous 
chloride  and  partly  oxidized  by  the  dichromate  and  hence  yield 
high  results.  If  solutions  containing  either  copper,  antimony  or 
titanium  are  reduced  by  hydrogen  sulfide  instead  of  stannous 
chloride,  correct  results  can  be  obtained,  since  the  two  first- 
named  elements  are  precipitated  and  can  be  removed  by  filtra- 
tion, and  the  last  is  not  reduced. 

Outline  of  Method  for  an  Easily  Soluble  Hematite  or  Magne- 
tite Ore.  Weigh  out  1  gm.  of  the  finely  ground  sample  into  a 
covered  beaker,  introduce  20  cc.  of  concentrated  hydrochloric 
acid  and  about  five  drops  of  stannous  chloride  solution,  cover  with 
a  watch  glass,  and  allow  to  digest  on  a  sand  bath  until  the  residue 
is  a  pure  white  color.  Rinse  the  cover  and  sides  of  the  beaker  and 
transfer  the  solution  to  a  100  cc.  graduated  flask.  Cool  to  room 
temperature,  dilute  to  exactly  100  cc.  and  mix  thoroughly. 

Remove  25  cc.  of  the  solution  to  a  200  cc.  beaker  by  means  of 
a  pipet,  add  5  cc.  of  dilute  hydrochloric  acid,  heat  to  boiling,  and 
then  add  stannous  chloride  solution  a  drop  at  a  time  until  the 
solution  is  colorless,  but  carefully  avoid  adding  more  than  one 


DETERMINATIONS  WITH  POTASSIUM   BICHROMATE       335 

drop  in  excess.  Cool  the  solution  slightly,  add  50  cc.  of  water  and 
then  10  cc.  of  a  saturated  solution  of  mercuric  chloride.  This 
should  produce  a  white,  crystalline,  precipitate  of  mercurous  chlo- 
ride; if  it  does  not  do  so  an  insufficient  amount  of  stannous 
chloride  was  used;  if  the  precipitate  is  black  or  gray  too  much 
was  used  and  the  results  will  probably  be  too  high. 

Titrate  with  the  dichromate  solution  as  in  the  standardization, 
adding  it  in  quantities  of  2  cc.  until  the  tests  show  a  change  from 
a  deep  blue  to  a  light  blue,  then  add  the  titrating  solution  until 
the  proper  end-point  has  been  reached.  With  some  experience 
it  is  possible  to  obtain  a  good  end-point  with  the  first  portion  of 
solution  used;  beginners  usually  find  it  necessary  to  titrate  a 
second  portion,  profiting  by  the  experience  previously  gained. 
Calculate  the  per  cent  of  iron  present. 

Determination  of  Iron  in  a  Difficultly-soluble  Ore.  Weigh  out 
into  a  20  cc.  glazed  porcelain  crucible  approximately  3  gm.  of 
sodium  peroxide,  avoiding  the  white  crust  often  found  on  the 
surface,  which  consists  largely  of  sodium  carbonate  and  which,  in 
addition  to  being  less  efficient  in  its  action  on  the  ore,  has  a  much 
higher  melting  point.  Weigh  out  accurately  1  gm.  of  the  finely 
powdered  ore,  add  to  the  crucible  and  mix  with  the  peroxide  with 
a  platinum  wire  or  glass  rod.  Place  the  crucible  on  a  gauze,  heat 
slowly  until  its  contents  fuse  and  keep  at  that  temperature  for  ten 
minutes;  this  should  produce  a  clear  but  deeply  colored  molten 
mass. 

Allow  the  crucible  to  cool,  distributing  the  molten  mass  over  its 
inner  surface  by  carefully  tipping  and  rotating  during  solidification. 
Place  the  crucible  in  an  evaporating  dish,  add  50  cc.  of  water  and 
slowly  introduce  an  excess  of  hydrochloric  acid.  Remove  and 
rinse  off  the  crucible,  heat  the  solution  to  boiling  to  decompose 
the  hydrogen  peroxide  formed,  then  transfer  to  a  100  cc.  graduated 
flask  and  treat  as  in  the  analysis  of  easily  soluble  ores. 

The  method  outlined  assumes  that  neither  copper  nor  any  of 
the  other  metals  which  affect  the  result  are  present. 


336  QUANTITATIVE   CHEMICAL  ANALYSIS 

IV.   DETERMINATION  OF  CHROMIUM  IN  CHROMITE 

Theory  of  the  Process.  The  reaction  between  a  soluble  chro- 
mate and  a  ferrous  salt  can  also  be  used  for  the  determination  of 
the  former  by  using  the  method  of  back  titration,  that  is,  by 
adding  an  excess  of  a  standard  solution  of  ferrous  salt  and  then 
titrating  with  a  standard  dichromate  solution.  Since  all  com- 
pounds of  chromium  are  readily  converted  into  soluble  sodium 
chromate  by  fusing  with  sodium  peroxide  the  method  is  widely 
applicable  for  the  determination  of  this  element. 

The  mineral  chromite  consists  of  ferrous  oxide  combined  with 
the  sesquioxide  of  chromium,  but  many  samples  also  contain 
magnesium,  aluminum,  silicon,  and  sometimes  manganese  and 
nickel.  When  fused  with  sodium  peroxide,  chromates,  ferrates, 
aluminates,  silicates  and  manganates  of  sodium,  also  oxide  of 
magnesium  and  peroxide  of  nickel,  if  this  element  is  present  or  if 
the  fusion  is  made  in  a  nickel  crucible,  are  produced.  The  fused 
mass  is  readily  disintegrated  by  treatment  with  water,  especially 
if  an  excess  of  peroxide  is  present.  The  chromate  and  most  of 
the  silicate  and  aluminate  dissolve  readily;  the  permanganate  also 
dissolves  unless  an  excess  of  peroxide  is  present,  the  ferrate  hy- 
drates and  forms  insoluble  ferric  oxide  or  hydroxide;  the  magne- 
sium and  nickel  oxides  remain  insoluble.  Hence  by  digesting  the 
fused  mass,  filtering  off  and  washing  the  resulting  precipitate  a 
solution  which  contains  all  of  the  chromium  as  sodium  chromate, 
and  no  substances  which  possess  strong  oxidizing  or  reducing 
properties  except  the  excess  of  sodium  peroxide  used,  is  obtained. 
The  peroxide  is  readily  decomposed  by  heating  the  solution  to 
boiling.  There  is  evidently  no  objection  to  making  the  fusion  in 
a  nickel  crucible. 

Outline  of  Method  of  Procedure.  Weigh  out  about  4  gm.  of 
sodium  peroxide,  which  should  not  contain  much  carbonate,  into 
a  30  cc.  nickel  crucible.  Weigh  out  one-half  gram  of  the  finely 
ground  ore,  add  to  the  crucible  and  mix  thoroughly  with  the 


DETERMINATIONS  WITH   POTASSIUM   BICHROMATE       337 

peroxide  by  means  of  a  glass  rod.  Place  the  crucible  on  a  wire 
gauze,  heat  until  the  mass  fuses  to  a  liquid  and  keep  at  this  tem- 
perature for  ten  minutes.  Decomposition  of  the  sample  will  be 
greatly  facilitated  by  seizing  the  crucible  with  a  pair  of  tongs  and 
gently  rotating  the  contents.  The  resulting  liquid  mass  will  be 
of  a  dark  red  color  and  contain  much  suspended  nickel  oxide. 

Allow  the  crucible  to  cool,  distributing  the  contents  around  the 
sides  during  solidification,  then  place  in  a  capacious  evaporating 
dish  and  add  100  cc.  of  water.  Heat  slowly  to  boiling  and  stir 
until  the  fused  mass  is  completely  disintegrated;  remove  the 
crucible  from  the  dish  and  rinse  it  off;  filter  the  resulting  mixture 
thru  all  cm.  filter,  receiving  the  filtrate  into  a  250  cc.  graduated 
flask,  and  wash  until  the  precipitate  is  free  from  soluble  chromate. 
Cool  the  solution  in  the  flask  and  dilute  to  exactly  250  cc. 

Measure  out  50  cc.  of  the  solution,  acidify  with  hydrochloric 
acid,  and  add  5  cc.  of  the  concentrated  acid  in  excess;  next  add 
50  cc.  of  an  approximately  one-tenth  normal  solution  of  ferrous 
sulfate,  and  finally  titrate  with  the  standard  dichromate  solution. 
Titrate  also  a  second  50  cc.  portion  of  the  ferrous  sulfate  solution 
directly  with  the  dichromate  solution.  The  difference  between 
the  amounts  of  dichromate  solution  used  in  the  two  titrations 
corresponds  to  the  chromic  acid  formed  from  one-fifth  of  the  ore 
weighed  out.  Calculate  the  percentage  of  chromium  present. 

V.   QUESTIONS  AND  PROBLEMS.     SERIES  23 

1.  In  the  standardization  of  a  solution  of  potassium  dichromate  a  solution 
of  a  ferrous  salt,  which  has  a  volume  of  100  cc.  and  contains  0.2  gm.  of  iron, 
is  used.     In  titrating  an  ore  with  the  same  solution  0.2  gm.  of  iron  is  again 
present,  but  the  solution  has  a  volume  of  600  cc.     If  the  indicator  used  per- 
mits of  the  recognition  of  one  part  of  ferrous  iron  in  100,000,  what  error 
results  from  the  fact  that  the  two  titrations  are  made  at  different  volumes? 

2.  What  error  might  be  expected  in  a  determination  of  iron  in  an  ore 
containing  forty  per  cent  of  iron  and  two-tenths  of  a  per  cent  of  copper, 
assuming  that  the  copper  is  completely  reduced  by  the  stannous  chloride  and 
reoxidized  by  the  dichromate? 


338  QUANTITATIVE  CHEMICAL  ANALYSIS 

3.  If  acetic  acid  is  substituted  for  hydrochloric  in  titrating  the  iron  solu- 

7tion,  what  volume  of  80  per  cent  acid  would  have  to  be  added  for  each  100  cc. 
of  total  volume  to  equal  5  cc.  of  concentrated  hydrochloric  acid  for  the  same 
volume,  assuming  that  the  dissociation  constant  of  the  acetic  is  1.8  X  10"5  and 
that  of  hydrochloric  acid  is  1.  £V>ic,V£&*  /.*-  -r  ^$49^  H& 

4.  Write  out  all  of  the  reactions  involved  in  the  determination  of  chromium 
in  chromite  which  contains,  in  addition  to  iron  and  chromium,  aluminum, 

manganese  and  nickel. 
*'. 

6.   Outline  an  indirect  volumetric  method  for  the  determination  of  lead 

which  makes  use  of  a  standard  solution  of  potassium  dichromate. 


CHAPTER  XLVII 

DETERMINATIONS  WITH  IODINE  AND   SODIUM  THIOSULFATE 
I.  GENERAL  FEATURES  OF  IODOMETRIC  PROCESSES 

Typical  Reactions.  Iodine  acts  directly  as  an  oxidizing  agent 
by  taking  up  a  negative  charge  and  forming  the  iodine  ion  as  rep- 
resented by 

(1)  2  Fe  +  4  Cl  +  I2  ->  2  Fe  +  4  Cl  +  2 1 
and 

(2)  1  4Na  +  2S~263  +  I2->4Na  +  S406  +  21, 

or  indirectly,  by  reacting  with  water  to  form  both  iodine  and 
hydrogen  ions  and  thus  rendering  the  oxygen  of  the  water  available 
as  an  oxidizing  agent,  as  represented  by: 

(3)  3  H  +  As63  +  I2  +  H20  ->  5  H  +  As64  +  21. 

Of  these  reactions  (1)  is  practically  complete,  (2)  is  complete  in 
a  neutral  solution  and  (3)  can  be  made  complete  in  either  direc- 
tion by  varying  the  concentration  of  hydrogen  ion. 

In  the  presence  of  even  small  concentrations  of  a  strong  base 
iodine  acts  very  differently  since  it  is  itself  oxidized  to  I03  ions  as 
represented  by  the  equation 

(4)  6  K  +  6  HO  +  3 12  ->  6  K  +  5 1  +  IO3  +  3  H20. 

The  equilibrium  constant  of  this  reaction  is  small  and  altho  it 
cannot  be  made  the  basis  of  a  quantitative  process  it  often  pre- 
vents the  use  of  iodine  as  an  oxidizing  agent  in  solutions  which 
contain  appreciable  concentrations  of  hydroxyl  ions. 

339 


340  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  table  of  electrode  potentials  on  page  312  indicates  that  the 
oxidizing  potential  of  iodine  is  decidedly  less  than  that  of  per- 
manganates and  chromates,  and  of  chlorine  and  bromine.  Ex- 
perience shows  that  in  the  presence  of  a  sufficient  concentration 
of  hydrogen  ion  all  of  these  reagents  oxidize  the  iodine  ion  to  free 
iodine  according  to  reactions,  similar  to  (5),  which  are  practically 
irreversible. 

(5)      12  K  +  2  Mn04  +  10  I  +  16  H  +  16  Cl-*5  I2  +  12  K 
+  16Cl  +  2Mn  +  8H20. 


Idometric  Processes.  The  facts  outlined  above  suggest  two 
classes  of  reactions  which  could  be  used  as  the  basis  of  volumetric 
processes.  In  the  first  class  certain  reactions  which  involve  the 
use  of  a  standard  solution  of  iodine,  which  acts  either  directly  or 
indirectly  as  an  oxidizing  agent  in  either  a  neutral  or  acid  solution, 
are  used  for  the  determination  of  certain  substances  commonly 
classed  as  reducing  agents.  Since  the  degree  of  oxidation  of  the 
iodine  in  all  of  these  reactions  changes  from  0  to  —  1,  its  oxidiz- 
ing capacity  is  always  1.  In  the  second  class  certain  substances, 
which  are  usually  classed  as  oxidizing  agents,  are  determined 
indirectly  by  causing  them  to  react  with  an  acidified  solution  of 
a  soluble  iodide  and  titrating  the  iodine  liberated  with  a  solution 
of  a  reducing  agent.  Both  classes  of  processes  are  included  under 
the  term  "iodometric." 

Preparation  of  an  Iodine  Solution.  The  solubility  of  iodine  in 
water  is  too  small  to  make  the  preparation  of  even  one-tenth  nor- 
mal solutions  possible.  In  the  presence  of  an  excess  of  potassium 
iodide  an  unstable  but  soluble  periodide  of  the  formula  KI3  is 
formed,  which,  in  the  presence  of  reducing  agents,  decomposes  so 
readily  into  potassium  iodide  and  free  iodine  that  it  can  be  used 
as  though  it  were  a  simple  solution  of  iodine.  Solid  iodine  is 
readily  dissolved  by  concentrated  but  not  byxlilute  solutions  of 
potassium  iodide  and  when  a  solution  of  the  periodide  has  been 


IODINE  AND   SODIUM   THIOSULFATE  341 

prepared  in  this  manner  it  can  be  diluted  up  to  a  certain  limit 
without  causing  free  iodine  to  separate.  The  solution  of  iodine 
in  potassium  iodide  probably  contains  in  addition  to  normal 
iodine  ions,  ions  of  the  formula  I3. 

Preparation  of  a  Standard  Reducing  Agent.  A  standard  solu- 
tion of  a  reducing  agent,  which  reacts  completely  with  the  iodine 
solution  can  be  used  to  advantage  for  the  readjustment  of  the 
standard  of  this  solution,  as  it  is  much  less  stable  than  potassium 
permanganate;  it  is  also  necessary  for  processes  based  upon  re- 
actions similar  to  (5).  Sodium  thiosulfate  is  by  far  the  most 
satisfactory  reagent  for  this  purpose,  as  it  is  comparatively  stable 
if  the  solution  is  kept  neutral  altho  it  is  slowly  decomposed  by  the 
carbon  dioxide  absorbed  from  the  air  if  left  exposed. 

Determination  of  the  End-Point.  A  single  drop  of  one-tenth 
normal  iodine  solution  imparts  an  appreciable  color  to  200  cc.  of 
water  and  in  many  of  the  titrations  made  with  this  solution  no 
indicator  is  necessary.  If  the  solution  titrated  contains  other 
color-yielding  substances,  or  if  greater  accuracy  is  demanded,  a 
solution  of  starch  should  be  used  as  an  indicator.  Under  favor- 
able conditions  the  presence  of  one  part  of  free  iodine  in  several 
million  can  be  recognized,  by  this  indicator,  but  the  delicacy  of  the 
test  and  the  character  of  the  color  produced  are  affected  by  a 
number  of  factors.  It  is  decidedly  less  delicate  when  the  concen- 
tration of  iodine  ions  and  of  hydrogen  ions  is  very  small.  If  the  con- 
centration of  the  free  iodine  present  is  large  as  compared  with  that 
of  the  starch,  the  solution  has  a  green  color;  if  this  ratio  is  smaller 
it  has  a  blue  color;  if  the  solution  contains  a  large  concentration 
of  bicarbonates  it  has  a  reddish  color. 

Standardization  of  the  Iodine  Solution.  The  iodine  solution 
can  be  standardized  by  titrating  against  a  previously  standardized 
thiosulfate  solution,  or  against  a  weighed  amount  of  arsensious 
oxide  or  potassium  antimonyl  tartrate  (tartar  emetic).  Owing 
to  the  ease  with  which  it  can  be  purified  by  sublimation  the  former 
substance  is  more  generally  used. 


342  QUANTITATIVE  CHEMICAL  ANALYSIS 

Since  the  action  of  the  iodine  solution  is  actually  due  to  the  Is 
ions  which  it  contains,  the  reaction  upon  which  this  method  of 
standardization  is  based  is  properly  represented  by  the  expression 

(6)       3H+  As63  +  K  +  I8  +  H20  ^5H  +  As64  +  K  +  31. 

The  equilibrium  constant  for  this  reaction  has  been  found  *  to  have 
the  value  0.07  at  25°  and  therefore  that 

(As04)  -5-  (As03)  =  (0.07)  •  (I8)  4-  (H)2  -  (I)*. 

The  only  factor  which  can  be  varied  for  the  purpose  of  displacing 
the  equilibrium  in  the  desired  direction  and  making  the  ratio 

(AsO4)  -*•  (As03)  very  large  is  (H).  Evidently  (H)  must  be  made 
small  as  compared  with  0.07  if  the  oxidation  of  all  the  arsenic 
present  is  to  be  made  reasonably  complete  when  an  equivalent 
amount  of  iodine  solution  has  been  added.  Since  hydrogen  ions 
are  formed  as  the  reaction  progresses  it  is  also  necessary  to  intro- 
duce some  reagent,  like  sodium  bicarbonate,  which  will  keep  the 
concentration  of  hydrogen  ions  small  and  which  does  not  yield 
sufficient  concentrations  of  hydroxyl  ions  to  cause  reaction  (4)  to 
take  place.  Experience  has  shown  that  the  proper  conditions  are 
maintained  if  the  solution  has  a  volume  of  75  cc.,  if  it  is  made 
neutral  to  phenolphthalein  and  if  2.5  gm.  of  pure  sodium  bicarbo- 
nate is  added  and  the  solution  saturated  with  carbon  dioxide. 

II.   CLASSIFICATION  OF  IODOMETRIC  PROCESSES 

Determination  of  Substances  Oxidized  by  Iodine.  Under  this 
head  are  included  the  element  tin,  which  is  oxidized  from  the  bi- 
to  the  quadrivalent  condition  even  in  the  presence  of  acids,  and 
arsenic  and  antimony,  which  are  oxidized  from  the  tri-  to  the  quin- 
quivalent condition  under  the  conditions  noted  in  the  preceding 
paragraph.  Under  the  same  head  arc  included  sulfurous  acid 
which  is  oxidized  to  sulfuric  acid  in  neutral  or  acid  solutions; 
*  Washburn,  Jour,  of  Am.  Chem.  Soc.,  30,  31  (1908). 


IODINE  AND   SODIUM   THIOSULFATE  343 

hydrogen  sulfide,  which  is  oxidized  to  sulfur  and  hydriodic  acid 
under  similar  conditions;  thiosulfuric  acid,  which  is  oxidized  to 
tetrathionic  acid  (see  reaction  2)  under  similar  conditions;  and 
salts  of  hydrocyanic  acid,  which  are  oxidized  to  cyanogen  iodide 
and  a  salt  of  hydriodic  acid  in  a  neutral  solution. 

Determination  of  Substances  Reduced  by  Hydriodic  Acid. 
Three  factors  can  be  varied  for  the  purpose  of  making  reactions 
similar  to  (5)  sufficiently  complete  and  rapid  to  make  the  deter- 
mination of  oxidizing  agents  possible.  First,  a  large  amount  of  a 
soluble  iodide  may  be  added  for  the  purpose  of  making  the  con- 
centration of  the  iodide  ions  large.  Thus  reaction  (1)  may  be 
made  to  proceed  in  the  reverse  direction  to  such  an  extent  as  to 
make  it  useful  in  the  determination  of  ferric  salts  by  the  use  of  a 
large  excess  of  potassium  iodide. 

Second,  the  concentration  of  the  hydrogen  ion  can  be  made  large 
by  the  addition  of  a  strong  acid.  Thus  altho  chlorine  and  bro- 
mine are  completely  reduced  by  moderate  concentrations  of  sol- 
uble iodides,  cupric  salts,  also  permanganates  and  chromates,  are 
not  completely  reduced  unless  a  small  concentration  of  hydrogen 
ion  is  also  present  and  arsenates  and  antimonates  are  not  com- 
pletely reduced  unless  this  concentration  is  very  large. 

Third,  by  increasing  the  temperature  to  the  boiling  point  of  the 
solution  the  iodine  formed  is  volatilized  and  the  equilibrium  forced 
in  the  desired  direction.  Such  determinations  are  necessarily 
carried  out  in  a  distilling  apparatus,  in  which  all  of  the  iodine 
formed  is  distilled  into  a  receiver  before  being  titrated.  This 
device  has  been  successfully  used  in  the  determination  of  molyb- 
denum which  can  be  reduced  from  the  hexa-  to  the  trivalent 
condition. 

Indirect  lodometric  Determinations.  A  number  of  insoluble 
oxidizing  agents,  such  as  the  peroxides  of  manganese  and  lead, 
are  completely  reduced  by  concentrated  hydrochloric  acid  at 
moderately  high  temperatures  and  the  chlorine  produced  can  be 
distilled  into  a  solution  of  potassium  iodide,  and  the  resulting 


344  QUANTITATIVE   CHEMICAL  ANALYSIS 

iodine  titrated.  This  forms  the  basis  of  an  indirect  method  for 
the  determination  of  these  oxides  and  in  general  of  all  oxidizing 
agents  which  are  completely  reduced  under  these  conditions. 

A  second  series  of  indirect  processes  represents  combinations  of 
precipitation  and  oxidation  processes.  As  already  noted  chromic 
acid  and  its  salts  can  be  determined  by  reducing  with  potassium 
iodide  and  titrating  the  resulting  iodine;  hence  those  metals  which 
form  insoluble  chromates  can  be  determined  by  adding  a  meas- 
ured volume  of  a  standard  solution  of  a  soluble  chromate,  filtering 
off  the  precipitate  formed  and  determining  the  soluble  chromate 
left  in  the  nitrate;  the  amount  of  metal  present  can  then  be  cal- 
culated from  the  difference  between  the  soluble  chromate  added 
and  that  found  in  the  filtrate. 

III.   OUTLINE  OF  METHOD  FOR  PREPARATION  OF  SOLUTION 

Preparation  of  Iodine  Solution.  Weigh  out  12.7  gm  of  pure 
iodine,  place  in  a  small  beaker,  add  20  gm.  of  potassium  iodide 
and  20  cc.  of  water  and  stir  occasionally  until  the  iodine  is  com- 
pletely dissolved.  Dilute  the  mixture  slowly  to  one  liter  and 
place  in  a  clean  bottle  made  of  colored  glass  or  one  which  is 
covered  with  opaque  paper. 

Preparation  of  Starch  Solution.  Place  about  a  gram  of  starch 
in  a  small  beaker,  add  about  20  cc.  of  water  and  stir  until  the 
mixture  is  smooth.  Heat  in  a  separate  beaker  200  cc.  of  water 
to  boiling,  pour  the  starch  mixture  into  it  and  boil  the  resulting 
mixture  for  three  minutes,  being  careful  to  prevent  any  of  the 
starch  from  settling  to  the  bottom  for  if  it  does  so  the  beaker 
will  crack.  Allow  the  mixture  to  stand  for  several  hours,  then 
decant  off  the  clear  portion. 

Standardization  of  Iodine  Solutions.  Weigh  out  0.2  gm.  of 
pure  arsenious  oxide,  dissolve  in  20  cc.  of  an  approximately  normal 
solution  of  sodium  hydroxide,  add  a  drop  of  phenolphthalein  and 
then  dilute  hydrochloric  acid  until  the  solution  is  just  colorless. 
Dilute  the  solution  to  75  cc.,  add  2.5  gm.  of  sodium  bicarbonate, 


IODINE  AND   SODIUM  THIOSULFATE  345 

and  pass  carbon  dioxide  thru  it  until  saturated.  Add  about  1  cc. 
of  the  starch  solution,  and  titrate  with  the  iodide  solution  added 
from  a  glass-stoppered  buret  until  the  mixture  acquires  a  faint 
but  permanent  rose  to  purple  color.  Calculate  the  relation  of  the 
solution  to  normal  strength,  assuming  that  the  reducing  power  of 
the  arsenious  oxide  is  four.  I 

Preparation  of  Thiosulfate  Solution.  Weigh  out  24.8  gm.  of 
pure  crystallized  sodium  thiosulfate  (Na2S203-5H20),  dissolve  and 
dilute  to  one  liter.  Measure  out  by  means  of  a  pipet  25  cc.  of  the 
iodine  solution,  dilute  to  75  cc.  and  titrate  with  the  thiosulfate 
solution.  It  will  be  found  desirable  to  add  the  latter  until  the 
mixture  has  a  very  faint  yellow  color  before  adding  the  starch 
indicator  and  then  to  continue  the  titration  until  the  mixture 
changes  from  blue  to  colorless.  Calculate  the  relation  which  the 
thiosulfate  solution  bears  to  normal  strength. 

IV.   DETERMINATION  OF  ARSENIC  IN  PARIS  GREEN 

Composition  of  Sample.  Paris  green  is  an  aceto-arsenite  of 
copper  which  is  largely  used  in  combating  insects  injurious  to 
cultivated  plants.  The  composition  of  commercial  samples  varies 
and  one  of  the  factors  which  determine  their  value  for  the  purpose 
indicated  is  the  percentage  of  arsenic  present. 

Theory  of  Method  Used.  Arsenic  can  be  determined  by 
oxidizing  it  from  the  tri-  to  the  quinquivalent  condition  with  a 
standard  solution  of  iodine,  or  by  reducing  it  from  the  quinqui- 
to  the  trivalent  condition  by  means  of  hydriodic  acid  and  titrat- 
ing the  liberated  iodine  with  a  solution  of  sodium  thiosulfate. 
When  Paris  green  is  treated  with  a  solution  of  sodium  hydroxide, 
cuprous  oxide,  sodium  acetate,  and  a  mixture  of  sodium  arsenite 
and  sodium  arsenate  are  produced.  The  insoluble  cuprous  oxide 
can  be  filtered  off  and,  the  arsenic  determined  in  the  filtrate  by 
reducing  it  to  the  quinquivalent  condition  with  hydriodic  acid  in  , 
a  strongly  acidified  solution,  reducing  the  liberated  iodine,  neu- 
tralizing the  solution  and  titrating  with  an  iodine  solution. 


346  QUANTITATIVE  CHEMICAL  ANALYSIS 

Outline  of  Method  of  Procedure.  Weigh  out  2  gm.  of  the 
sample  into  a  small  beaker,  add  25  cc.  of  a  normal  solution  of 
sodium  hydroxide,  heat  cautiously  for  some  five  minutes  or  until 
converted  into  bright  red  cuprous  oxide.  Rinse  the  mixture  into 
a  100  cc.  graduated  flask,  cool  and  dilute  to  exactly  100  cc.  and 
then  filter  thru  a  dry  filter,  rejecting  the  first  10  cc.  of  filtrate. 
Remove  25  cc.  of  the  filtrate  to  a  300  cc.  beaker,  add  15  cc.  of 
concentrated  hydrochloric  acid  and  2  gm.  of  potassium  iodide  and 
then  add  one-tenth  normal  sodium  thiosulfate  solution  until  the 
mixture  is  just  colorless.  As  the  volume  is  small  it  is  not  neces- 
sary to  use  an  indicator.  Next  add  40  cc.  of  water  and  one  drop 
of  phenolphthalein,  then  add  slowly  a  20  per  cent  solution .  of 
sodium  hydroxide  until  the  mixture  shows  a  faint  pink  color. 
Acidify  with  a  drop  of  dilute  hydrochloric  acid,  add  2.5  gm.  of 
sodium  bicarbonate,  saturate  with  carbon  dioxide  and  titrate  with 
iodine  solution  as  in  the  standardization.  Calculate  the  percent- 
age of  As203  present. 

V.   DETERMINATION  OF  COPPER  IN  BRASS 

Theory  of  Method.  All  soluble  cupric  salts  react  with  potas- 
sium iodide  in  neutral  or  slightly  acid  solutions  as  represented  by 

(7)  2  CuS04  +  4  KI  ->  2  Cul  +  2  K2S04  +  I2. 

The  fact  that  cuprous  iodide  is  very  insoluble  and  that  cupric 
iodide  is  very  unstable  gives  the  equilibrium  constant  of  this  reac- 
tion a  large  value.  The  most  favorable  conditions  are  the  presence 
of  from  3  to  5  per  cent  of  potassium  iodide  and  about  3  per  cent 
by  volume  of  concentrated  hydrochloric  acid.  With  a  smaller 
concentration  of  hydrogen  ion  the  reaction  is  slower  and  the  end- 
points  less  distinct.  The  presence  of  large  concentrations  of 
soluble  salts  especially  of  acetates  seem  to  retard  the  reaction; 
the  reason  for  this  is  not  apparent. 

When  brass  is  dissolved  in  nitric  acid  small  amounts  of  nitrous 
acid  are  produced;  as  this  reagent  slowly  liberates  iodine  from 


IODINE  AND   SODIUM   THIOSULFATE  347 

potassium  iodide  it  must  be  expelled  by  evaporation  or  oxidized 
by  bromine  or  hydrogen  peroxide  before  making  the  titration. 

Outline  of  Method  of  Procedure.  Weigh  out  0.3  gm.  of 
sample  into  a  200  cc.  beaker,  add  10  cc.  of  dilute  nitric  acid,  cover 
with  a  watch  glass  and  warm  .gently  until  the  metal  dissolves. 
Remove  the  cover,  rinse  its  under  side  with  water  and  evaporate 
the  solution  to  about  3  cc.  Dissolve  basic  salts  if  such  have 
separated  with  a  few  drops  of  nitric  acid  and  dilute  to  50  cc.  Add 
sufficient  ammonium  hydroxide  to  produce  a  clear  bright  blue 
solution,  then  neutralize  with  hydrochloric  acid  and  add  3  cc.  of 
the  dilute  acid  in  excess. 

Cool  the  solution  to  25°,  add  3  gm.  of  potassium  iodide  and  stir 
until  dissolved.  Titrate  with  the  thiosulfate  solution  until  the 
mixture  has  a  light  yellow  color  only,  then  add  starch  solution 
and  continue  the  titration  until  the  light  blue  or  lilac  color  of  the 
mixture  fades  to  a  nearly  pure  white  and  does  not  regain  a  per- 
ceptible blue  color  after  three  minutes.  Calculate  the  percentage 
of  copper  present. 

VI.   DETERMINATION  OF  COPPER  IN  A  CHALCOPYRITE  ORE 

Interfering  Elements.  These  ores  usually  contain  in  addition 
to  copper  and  iron  sulfides  small  amounts  of  lead,  zinc  and  arsenic 
sulfides.  When  dissolved  in  nitric  acid  the  iron  is  oxidized  to  the 
trivalent  and  the  arsenic  to  the  quinquivalent  condition.  As 
both  elements  are  reduced  by  hydriodic  acid  it  is  necessary  to 
separate  the  copper  before  using  this  method.  Small  amounts  of 
lead  and  even  large  amounts  of  zinc  have  no  effect  upon  the 
process. 

Separation  of  Copper  by  Metallic  Aluminum.  The  oxidizing 
potential  of  cupric  salts  is  large  as  compared  with  that  of  metals 
like  zinc,  magnesium  and  aluminum,  and  under  certain  conditions 
it  is  possible  to  separate  copper  from  such  solutions  completely  by 
means  of  these  metals.  Aluminum  is  to  be  preferred  for  this  pur- 
pose owing  to  the  slowness  with  which  it  is  attacked  by  moderately 


348  QUANTITATIVE  CHEMICAL  ANALYSIS 

strong  solutions  of  sulfuric  acid.  The  separation  of  copper  by 
this  metal  is  retarded  by  ferric  iron,  which  is  reduced  to  the  ferrous 
condition  before  the  copper  begins  to  separate.  It  is  rendered 
incomplete  by  the  presence  of  even  small  concentrations  of  nitric 
acid.  It  is  most  rapid  when  the  solution  is  kept  hot  and  enough 
sulfuric  acid  is  present  to  cause  the  formation  of  sufficient  hydro- 
gen to  stir  the  solution  vigorously.  Under  these  conditions  all  of 
the  copper,  most  of  the  lead  and  a  part  of  the  arsenic  but  none  of 
the  zinc  and  iron  are  precipitated.  The  small  amount  of  arsenic 
which  may  separate  with  the  copper  does  not  affect  the  final  titra- 
tion  appreciably  if  the  solution  is  acidified  with  acetic  instead  of 
hydrochloric  acid. 

Outline  of  Method  of  Procedure.  Weigh  out  1  gm.  of  the  ore 
into  a  200  cc.  Erlenmeyer  flask,  add  5  cc.  of  concentrated  nitric 
acid  and  warm  until  violent  action  is  over,  next  add  10  cc.  of 
concentrated  hydrochloric  acid  and  evaporate  until  the  volume 
has  been  reduced  to  one-half,  then  cool,  add  very  cautiously  8  cc. 
of  concentrated  sulfuric  acid,  and  evaporate  until  the  flask  is  filled 
with  dense  white  fumes  of  sulfur  trioxide.  Cool  the  flask,  add 
30  cc.  of  water  and  allow  to  stand  with  occasional  shaking  until 
all  the  soluble  salts  have  been  brought  into  solution.  Transfer 
the  solution  to  a  200  cc.  beaker,  retaining  the  insoluble  matter 
as  far  as  possible  in  the  flask  but  washing  the  latter  thoroughly; 
the  final  volume  should  not  exceed  70  cc. 

Add  to  the  solution  a  strip  of  aluminum  foil  3  cm.  wide  and 
15  cm.  long,  which  has  been  bent  into  the  form  of  the  letter  S, 
heat  to  80°  and  set  aside  in  a  warm  place  until  the  copper  has  been 
completely  precipitated,  which  usually  requires  ten  minutes  more 
than  the  time  necessary  to  decolorize  the  solution.  Next  add 
10  cc.  of  water  saturated  with  hydrogen  sulfide,  and  if  the  solution 
remains  colorless  or  acquires  a  faint  brown  coloration  only  filter  at 
once,  using  a  small  filter  and  retaining  as  much  of  the  precipitated 
copper  in  the  beaker  as  possible.  Wash  the  precipitate  three 
times  with  10  cc.  portions  of  hydrogen  sulfide. 


IODINE  AND  SODIUM  THIOSULFATE  349 

Place  the  beaker  containing  the  precipitate  under  the  funnel 
and  pour  over  the  filter  about  10  cc.  of  warm  dilute  nitric  acid, 
moving  the  beaker  in  such  a  manner  as  to  cause  the  acid  solution 
to  flow  over  the  surface  of  the  aluminum  plate  and  dissolve  the 
small  amount  of  adhering  precipitate.  Replace  the  beaker  by  the 
flask  used  to  dissolve  the  ore  which  has  in  the  meantime  been 
cleaned.  Warm  the  solution  in  the  beaker  until  all  of  the  pre- 
cipitate has  been  dissolved,  then  remove  and  rinse  the  aluminum 
plate,  pour  the  solution  thru  the  filter  and  wash  free  from  copper. 

Add  10  cc.  of  bromine  water  to  the  flask  and  boil  vigorously 
until  the  excess  added  is  expelled.  Cool  the  solution,  make  alka- 
line with  ammonium  hydroxide,  acidify  with  acetic  acid  and  then 
add  3  cc.  of  the  dilute  acid  in  excess.  The  solution  should  have  a 
volume  not  greatly  exceeding  60  cc. 

Add  3  gm.  of  potassium  iodide  and  titrate  as  in  the  previous 
determination,  remembering  that  slightly  more  time  must  be 
allowed  for  the  mixture  to  come  to  equilibrium  owing  to  the 
smaller  concentration  of  hydrogen  ion  present. 

VII.   QUESTIONS  AND  PROBLEMS.     SERIES  24 

1.  A  solution  contains  0.1  gm.  of  H3AsO4  and  1  gm.  of  HC1,  and  has  a 
volume  of  100  cc.;   if  3  gm.  of  potassium  iodide  is  added  and  it  is  assumed 
that  the  potassium  iodide  and  the  three  acids  are  completely  dissociated, 
what  fraction  of  the  H3AsO4  is  reduced? 

2.  Write  out  all  of  the  reactions  involved  in  the  determination  of  arsenic 
in  Paris  green. 

3.  What  amount  of  acetic  acid  should  be  present  in  100  cc.  of  solution  in 
7  order  to  give  a  hydrogen  ion  concentration  equal  to  that  in  a  solution  contain- 
.    ing  3  cc.  of  concentrated  hydrochloric  acid  per  100  cc.  of  solution? 

'• 


SECTION  X 
PHYSICO-CHEMICAL  PROCESSES 


CHAPTER  XLVIII 

THEORY   OF  PHYSICO-CHEMICAL  METHODS 

Uses  of  Physical  Constants.  The  analyst  often  finds  it  de- 
sirable to  determine  certain  physical  constants  of  substances  sub- 
mitted to  him,  usually  with  one  of  three  objects  in  view.  First, 
for  the  purpose  of  identifying  or  characterizing  such  substances. 
Use  is  here  made  of  the  well-established  principle  that  the  physical 
constants  of  every  pure  substance  are  definite  magnitudes,  whose 
values  are  often  changed  materially  by  the  presence  of  small 
amounts  of  impurities;  the  extended  uses  made  of  the  melting- 
points  of  solids  and  of  the  boiling-points  of  liquids  for  this  purpose 
are  good  illustrations.  Second,  to  determine  whether  the  com- 
position of  the  substance  lies  within  the  limits  which  characterize 
the  class  of  substances  to  which  it  is  supposed  to  belong;  especially 
for  the  detection  of  adulterations  in  certain  food  products,  or  other 
substances  of  natural  origin,  which  are  complex  mixtures.  Third, 
for  the  determination  of  the  percentage  composition  of  certain 
mixtures,  which  can  be  analyzed  by  such  methods  more  easily  or 
more  accurately  than  by  methods  which  are  purely  chemical. 

Analysis  of  Mixtures  With  Additive  Properties.  The  quanti- 
tative analysis  of  mixtures  by  physico-chemical  methods  involves 
an  accurate  measurement  of  some  physical  property  of  the  sample, 
and  comparison  of  this  result  with  the  corresponding  physical 
constants  of  the  pure  components  of  the  mixture,  or  with  a  series 

350 


THEORY  OF  PHYSICO-CHEMICAL  METHODS  351 

of  constants  representing  similar  mixtures  of  known  composition. 
If  the  sample  is  a  simple  mechanical  mixture  of  two  components 
an  additive  relation  may  exist  between  certain  of  its  physical  con- 

JE7 

stants  and  those  of  the  two  components,  that  is,  -7=  is  a  constant 

where  dE  and  dP  represent  correlated  changes  in  the  constant 
concerned,  and  the  percentage  of  one  of  the  constituents  in  the 
mixture.  In  some  cases  the  expression  has  a  constant  value  only 
when  P  represents  the  relation  between  the  number  of  molecules, 
of  one  constituent  and  the  total  number  of  molecules  in  the 
mixture;  in  other  cases  it  is  constant  when  P  represents  con- 
centration, that  is,  the  weight  of  one  constituent  per  unit  volume 
of  mixture. 

If  the  constant  found  for  such  a  mixture  is  represented  by  E, 
and  the  corresponding  constants  of  its  two  components  A  and  B 
are  represented  by  EI  and  E2,  the  additive  relationship  would 
require  that  xEi  +  (100  -  x)  E2  =  100  E  where  x  and  (100  -  x) 
represent  the  percentages  of  A  and  B  respectively.  The  value  of 
x  can  then  be  easily  calculated  by  the  use  of  the  derived  formula 

100  (E  -  E2) 


x  = 


—  E2 


The  accuracy  of  such  a  process  clearly  depends,  not  only  upon  the 
accuracy  with  which  the  three  constants  E,  EI  and  E2  are  deter- 
mined, but  also  upon  the  value  (Ei—  E2). 

Such  methods  cannot  be  used  for  the  analysis  of  mixtures  con- 
taining more  than  two  components  unless  one  or  more  of  the 
components  is  without  effect  upon  the  property  concerned. 
Theoretically  it  is  possible  to  analyze  mixtures  containing  three 
components  by  measuring  two  of  its  physical  constants,  formulat- 
ing two  equations  similar  to  that  already  given,  and  solving  these 
in  the  customary  manner. 

Mixtures  Whose  Properties  Are  Not  Additive.  Mixtures 
which  possess  purely  additive  properties  are  rare,  altho  the  de- 


352 


QUANTITATIVE  CHEMICAL  ANALYSIS 


partures  from  pure  additive  relationships  are  not  infrequently  so 
small  that  they  can  be  disregarded. 

Considering  first  solid  mixtures,  three  types  of  structural  units 
are  possible.  First,  the  two  substances  may  themselves  exist 
as  distinct  independent  structural  units;  second,  they  may  form 
one  or  more  series  of  solid  solutions  with  each  other,  each  with 

definite  saturation  limits ;  and 

Melting  Points  third,  they  may  form  one  or 

more  chemical  compounds, 
often  when  the  appearance 
of  the  mixture  gives  no  evi- 
dence of  chemical  changes 
having  taken  place.  Mixed 
types  are  also  possible,  that 
is,  the  pure  components  may 
form  solid  solutions  with  the 
compounds  and  the  com- 
pounds may  form  solid  solu- 
tions with  each  other. 

The  significance  of  these 
three  types  of  structure  in  the 
interpretation  of  the  physical 
constants  of  mixtures  is  illus- 
trated by  the  curves  shown  in  Fig.  62.  The  abscissas  here  represent 
the  relative  amounts  of  the  two  components  A  and  B  in  the  mixture, 
and  the  ordinates  the  temperatures  at  which  they  begin  to  solidify 
when  cooled  from  the  molten  condition.  Curve  I  illustrates 
mixtures  which  form  neither  solid  solutions  nor  compounds,  and  is 
characterized  by  a  distinct  break,  which  represents  the  so-called 
eutectic  point.  Curve  II  illustrates  mixtures  which  form  a  con- 
tinuous series  of  solid  solutions;  it  is  characterized  by  a  minimum, 
altho  certain  mixtures  of  this  type  show  a  maximum.  Curve  III 
illustrates  mixtures  which  form  a  single  stable  compound;  it  shows 
a  well-defined  cusp  at  the  point  which  represents  the  composition 


Composition  of  Mixture 

Fig.  62.  —  Melting  Points  of  Mixtures  of 
Two  Solids 


THEORY  OF  PHYSICO-CHEMICAL  METHODS  353 

of  the  compound.  The  corresponding  curves  for  mixtures  which 
show  mixed  types  of  structure  are  still  more  complex,  but  can  be 
easily  interpreted  from  the  relations  found  in  the  simpler  cases. 

The  factors  which  affect  the  physical  properties  of  liquid  mix- 
tures are  the  possible  association  of  the  molecules  of  the  solvent, 
the  formation  of  molecular  complexes,  especially  hydrates  and 
double  salts,  and  the  electrolytic  dissociation  of  the  solute.  The 
relations  are  decidedly  simpler  than  where  solid  mixtures  are  con- 
cerned, and  the  curves  representing  many  of  the  physical  con- 
stants of  liquid  mixtures,  especially  where  there  is  no  dissociation, 
or  where  the  dissociation  is  nearly  complete,  are  straight  or  slightly 
curved  lines. 

Use  of  Interpolation  Methods.  In  all  cases  in  which  the  con- 
stant measured  is  not  an  additive  function  of  its  two  components, 
it  becomes  necessary  to  measure  this  property  for  a  sufficient  num- 
ber of  mixtures  containing  known  proportions  of  these  components 
before  it  can  be  used  for  the  analysis  of  unknown  mixtures.  The 
composition  of  the  unknown  mixture  is  then  determined  by  inter- 
polating the  value  found  between  the  proper  interval  in  the  table 
which  has  been  prepared.  If  the  relation  made  use  of  is  repre- 
sented by  a  curve  which  shows  a  maximum  or  a  minimum,  certain 
of  the  determinations  made  may  correspond  to  two  different  points 
on  it,  and  therefore  to  either  of  two  mixtures  whose  percentage 
composition  may  differ  greatly.  If  the  mixture  is  a  solid  this  is  a 
serious  difficulty,  but  if  it  is  a  liquid  the  composition  of  the  mixture 
under  examination  can  be  inferred  from  the  effect  produced  upon 
the  constant  by  increasing  the  dilution.  If  the  curve  shows  a 
maximum,  and  increasing  the  dilution  increases  in  the  value  of 
the  constant  employed,  the  mixture  represents  the  more  concen- 
trated of  the  two  in  question;  if  it  shows  a  minimum  the  reverse 
relationship  must  hold. 

The  error  involved  in  the  interpolation  depends  upon  the  form 
of  the  curve  at  different  intervals;  the  most  favorable  condition 
is  where  the  curve  forms  an  angle  of  45°  with  the  horizontal  axis. 


354  QUANTITATIVE  CHEMICAL  ANALYSIS 

Physical  Constants  Most  Largely  Used.  The  physical  con- 
stants largely  used  for  quantitative  determinations  are  the  specific 
gravity,  specific  volume,  colorific  absorption,  index  of  refraction, 
and  optical  activity.  A  number  of  others,  such  as  the  conduc- 
tivity for  electrical  energy,  are  used  more  rarely.  The  three  first 
named  will  be  considered  in  detail  in  the  subsequent  chapters. 

Index  of  Refraction.  This  is  defined  as  the  ratio  of  the  sine 
of  the  angle  of  incidence  to  that  of  the  angle  of  refraction,  when  a 
beam  of  light  passes  from  air  to  a  layer  of  the  medium  under  con- 
sideration. It  is  used  especially  for  the  analysis  of  liquid  solutions. 
The  refractometer  devised  by  Abbe  is  largely  used  for  such  deter- 
minations; it  is  based  upon  the  measurement  of  the  angle  at  which 
an  incident  beam  of  light  is  totally  reflected  when  it  passes  thru  a 
double  prism  which  is  made  of  glass  but  has  the  form  of  a  Nicol 
prism.  The  determination  consists  in  placing  a  drop  of  the  liquid 
between  the  two  parts  of  the  prism  and  rotating  its  position  in  a 
vertical  plane  until  a  shadow  is  cast  at  a  particular  position,  that 
is,  corresponds  to  the  cross-bar  of  a  telescope,  with  which  the  in- 
strument is  provided.  The  angle  thru  which  the  prism  is  turned 
is  read  on  a  scale  by  means  of  a  magnifying  glass  in  terms  of  re- 
fraction index  directly.  It  can  be  used  for  liquids  varying  from 
1.3  to  1.7  with  a  maximum  error  which  is  less  than  1  in  the  third 
decimal  place.  This  instrument  is  used  especially  for  the  exami- 
nation of  fats  and  oils  and  was  found  especially  satisfactory  for 
the  detection  of  adulterants  in  olive  oil  and  butter. 

The  instrument  of  Zeiss  is  based  on  the  same  principle,  altho 
the  mechanical  construction  and  method  of  making  the  measure- 
ment are  totally  different.  The  single  glass  prism  used  is  immersed 
in  a  small  beaker  containing  the  liquid  to  be  tested,  and  the  ob- 
served results  are  expressed  on  an  arbitrary  scale,  which  corre- 
sponds to  a  range  in  refractive  index  of  from  1.325  to  1.366. 

The  refractive  indices  of  aqueous  solutions  of  a  large  number  of 
organic  and  inorganic  compounds  have  been  found  to  bear  a 
simple  relation  to  their  concentration,  and  the  percentage  com- 


THEORY  OF  PHYSICO-CHEMICAL   METHODS 


355 


4290 
o  80 
I  70 


30 


10 


N 


position  of  a  large  number  of  such  solutions  can  be  determined  with 
the  aid  of  the  tables  showing  this  relation.  It  is  possible  to  analyze 
by  this  method  certain  mixtures  which  are  extremely  difficult  to 
analyze  by  any  other  method.  Mixtures  of  methyl  and  ethyl 
alcohol  are  good  illustrations.  The  curves  representing  the  re- 
fraction indices  of  aqueous 
solutions  of  these  compounds 
show  the  wide  divergence  rep- 
resented in  Fig.  63.  It  so  hap- 
pens that  the  specific  gravities 
of  aqueous  solutions  of  the  two 
alcohols  of  the  same  percentage 
composition  are  practically 
identical,  and  that  of  mixtures 
equal  the  sum  of  the  percent- 
ages of  the  two  alcohols  pres-  J  ; 
ent.  Hence  the  percentage 
composition  of  such  mixtures 
can  be  determined  by  compar- 
ing the  sum  of  the  two  per- 
centages, which  is  ascertained 
from  a  specific  gravity  determination,  with  the  difference  between 
the  refractive  indices  of  aqueous  solutions  of  the  two  alcohols 
corresponding  to  this  percentage.  The  accuracy  of  the  method 
is  evidently  at  a  maximum  when  the  divergence  between  the  two 
curves  is  greatest,  that  is,  when  the  sum  of  the  two  percentages 
exceeds  ninety.  The  uses  of  the  refractometer  in  quantitative 
work  are  extremely  varied  and  important.* 

Specific  Rotory  Power.  The  ability  to  rotate  the  plane  of  a 
beam  of  polarized  light  is  possessed  by  a  very  few  solid  substances, 
by  a  limited  number  of  organic  liquids,  and  by  solutions  of  those 
organic  compounds  which  contain  an  asymmetric  carbon  atom, 

*  See  Lythgoe,  Report  of  the  Eighth  International  Congress  of  Applied 
Chemistry,  Vol.  I,  p.  295  (1912). 


10    20    30    40     50     60    70     80    90   100 
Percentage  of  Alcohol  by  Weight 

of  Methyl  and  of  Ethyl  Alcohol 


356  QUANTITATIVE   CHEMICAL  ANALYSIS 

that  is,"  an  atom  which  is  directly  linked  with  four  different  ele- 
ments or  radicals.  In  some  cases  the  plane  is  turned  to  the  right 
and  in  others  to  the  left,  and  the  magnitude  of  the  effect  is  one  of 
the  specific  constants  of  all  such  substances  if  the  comparison  is 
made  under  identical  conditions.  It  can  be  measured  by  means 
of  a  polariscope,  of  which  a  large  number  of  different  forms  are  in 
use.  These  instruments  consist  of  two  Nicol  prisms  mounted  in 
the  same  horizontal  axis,  between  which  a  tube  of  known  length 
filled  with  the  liquid  under  examination  is  placed.  The  angle 
thru  which  one  of  the  Nicols  must  be  rotated  to  compensate  for 
the  rotation  of  the  liquid,  or  the  thickness  of  a  piece  of  optically 
active  quartz  necessary  to  compensate  for  it  is  measured  by  a 
variety  of  optical  devices. 

The  optical  activity  of  solutions  is  directly  proportional  to  the 
concentration  of  the  solution  and  the  length  of  the  column  thru 
which  the  polarized  beam  passes.  Hence  the  percentage  compo- 
sition of  any  solution  can  be  calculated  from  its  optical  activity, 
if  the  activity  of  one  solution  containing  a  known  concentration 
of  the  substance  concerned  is  known.  Further,  the  scale  of  the 
polariscope  used  can  be  so  marked  as  to  give  directly  the  percent- 
age of  any  one  desired  substance,  provided  the  solution  of  the 
sample  used  is  made  to  contain  a  specified  concentration  of  the 
sample  and  examined  in  a  tube  of  specified  length. 

One  decided  advantage  of  making  use  of  the  optical  activity 
of  solutions  for  quantitative  work  is  that  the  number  of  substances 
which  produce  this  effect  are  so  limited,  and  the  determination 
of  those  substances  which  do  possess  it  is  not  effected  by  the 
impurities  usually  present.  It  is  especially  useful  in  the  deter- 
mination of  the  different  sugars,  and  related  substances,  and  the 
identification  of  the  different  terpenes  and  essential  oils.  The 
subject  is  a  very  large  one  and  cannot  be  considered  in  detail 
here.* 

*  See  Browne,  Handbook  of  Sugar  Analysis. 


CHAPTER  XLIX 

PROCESSES  BASED   UPON  THE  DETERMINATION   OF  THE 

SPECIFIC   GRAVITY   OR  SPECIFIC   VOLUME   OF   SOLIDS 

OR   LIQUIDS 

I.   GENERAL  FEATURES  OF  THE  METHODS 

Definition   of   Specific   Gravity  and   Specific  Volume.    The 

"  specific  gravity"  of  solids  and  liquids  is  defined  as  the  ratio  be- 
tween a  mass  of  the  substance  concerned,  and  that  of  an  equal 
volume  of  water.  The  relation  thus  defined  is  not  a  definite  one 
unless  the  temperatures  at  which  both  the  measurements  con- 
cerned have  been  made  are  also  specified.  A  temperature  of  4° 
is  usually  adopted  for  the  measurement  of  the  standard  water 
volume,  but  it  is  customary  to  adopt  a  more  convenient  one, 
especially  15°,  20°  or  25°,  in  measuring  the  volume  of  the  substance 
compared  with  it.  The  temperatures  actually  used  are  conven- 

/20°\ 
iently  expressed  in  the  form  of  a  fraction;  that  is,  (r^o)  C.  is  used 


to  express  the  fact  that  the  water  was  measured  at  15°  C.,  and  the 
substance  concerned  at  20°  C. 

The  specific  gravity  of  substances  referred  to  water  at  any  speci- 
fied temperature  can  be  converted  into  the  equivalent  value  re- 
ferred to  water  at  4°  C.  by  multiplying  by  the  specific  gravity  of 
water  at  the  specified  temperature. 

Corrections  for  the  buoyant  effect  of  the  air  upon  the  masses 
determined,  and  for  the  expansion  of  glass  vessels  used,  thru  tem- 
perature changes,  are  not  necessary  unless  results  of  extreme 
accuracy  are  demanded. 

The  "  specific  volume"  of  solids  and  liquids  is  the  reciprocal  of 

357 


358 


QUANTITATIVE  CHEMICAL  ANALYSIS 


the  specific  gravity;  that  is,  it  is  the  volume  occupied  by  the  solid 
or  liquid,  as  compared  with  the  volume  occupied  by  an  equal  mass 
of  water. 

Methods  of  Determining  the  Specific  Gravity  of  Solids.  The 
chief  difficulty  encountered  in  determining  the  specific  gravity  of 
a  solid  is  to  devise  a  method  by  which  its  volume  can  be  deter- 

mined with  sufficient  accuracy.  It  is 
usually  determined  by  measuring  the 
buoyant  effect  which  some  liquid,  whose 
specific  gravity  is  known,  has  upon  it. 
The  method  of  procedure  is  represented 
in  Fig.  64.  The  object  A  is  suspended 
in  the  liquid  from  the  arm  of  a  balance 
by  means  of  a  piece  of  aluminum  wire, 
and  the  weight  necessary  to  counter- 
balance it  ascertained.  This  result  is 
then  corrected  by  determining  and  sub- 
tracting the  weight  necessary  to  counter- 
balance the  wire  used,  when  immersed 
to  the  same  depth.  The  difference  be- 

tween the  weight  of  the  object  in  air  w 
Fig.  64.  -Apparatus  for  De-  and  the  wei  ht  thug  measured  w  rep. 

,,  .,,      .  ,.      .  ,     v  . 

resents  the  weight  of  liquid  displaced, 

and  this.  difference  divided  by  the  specific 
gravity  of  the  liquid  used,  its  volume.  If  G  represents  this  specific 
gravity,  that  of  the  solid  can  be  calculated  from  the  formula 


termination  of  Specific  Grav- 
ity  of  Solids 


Sp.  Gr.  - 


—  w 


The  liquid  most  frequently  employed  is  water,  and  in  this  case  G 
has  the  value  one  if  the  unit  of  volume  to  which  the  specific  gravity 
is  to  be  referred  is  that  of  water  at  the  temperature  used.  If  the 
solid  is  dissolved  or  acted  upon  chemically  by  water  some  other 
liquid  must  be  used. 


THE  USE  OF   SPECIFIC   GRAVITY   METHODS  359 

In  using  this  method  large  errors  may  arise  from  small  bubbles 
of  air  which  adhere  to  the  immersed  sample  or  to  the  wire,  or  are 
retained  in  the  cracks  or  crevices  often  found  in  solid  mixtures. 
This  difficulty  can  be  avoided  by  placing  the  vessel  containing  the 
immersed  sample  under  a  bell  jar  and  exhausting 
the  air,  or  by  boiling  the  liquid  surrounding  the 
sample  until  all  the  air  has  been  expelled.  The  error 
in  determining  the  volume  is  always  greater  than 
that  involved  in  determining  the  weight  because  the 
movement  of  the  balance  beam  is  greatly  hampered 
by  the  resistance  against  the  movement  of  the  im- 
mersed solid  presented  by  the  liquid. 

If  the  solid  consists  of  small  masses  another 
method  must  be  used.  One  of  these  is  based  upon 
the  use  of  a  "pycnometer"  flask  similar  to  that 
represented  in  Fig.  65.  This  consists  of  a  small 
bottle,  which  is  provided  with  a  carefully-fitted  glass 
stopper,  pierced  by  a  capillary  opening  and  therefore 
capable  of  containing  a  definite  volume  when  filled  to  some  par- 
ticular mark  on  the  capillary.  The  weight  Wi  of  some  liquid, 
whose  specific  gravity  G  is  known,  which  is  contained  by  the  flask 
when  filled  to  the  mark  is  first  determined;  a  known  weight  w  of 
the  sample  is  then  introduced,  the  level  of  the  liquid  again  brought 
to  the  mark,  and  the  weight  w2  of  the  contents  of  the  flask  again 
determined.  The  volume  displaced  by  the  sample  must  equal 
(w  +  wl—w*)  +  G  and  the  specific  gravity  is  calculated  from  the 
formula 


Sp.Gr.-f 
[ 


w  +  w1  — 


Direct  Determination  of  the  Specific  Gravity  of  Liquids.     The 

specific  gravity  of  liquids  can  be  determined  more  readily  and 
more  accurately  than  that  of  solids.  The  relative  masses  of  equal 
volumes  of  the  liquid  concerned,  and  of  water,  can  be  determined 


360 


QUANTITATIVE  CHEMICAL  ANALYSIS 


directly  by  means  of  a  pycnometer  flask,  or  still  more  accurately 
by  the  Ostwald-Sprengel  tube  represented  in  Fig.  66.  This  tube 
is  successively  sucked  full  of  the  desired  liquids,  until  one  capillary 

is  completely  filled  and  the  other  is  filled 
to  the  indicated  mark,  and  then  accu- 
rately weighed.  The  accuracy  of  the  re- 
sult obtained  with  this  device  can  be 
increased  to  almost  any  desired  degree 
by  using  tubes  of  sufficient  capacity,  and 
using  the  proper  precautions  in  filling 
and  weighing.  An  error  of  one  in  the 
fourth  decimal  place  need  not 
be  exceeded  if  the  capacity  of 
the  tube  is  at  least  10  cc. 

The  Use  of  Hydrometers. 
Where  speed  is  of  more  im- 

Fig.  66.  -  Ostwald-Sprengel   portance   than    accuracy,   the 
Tube  ,    r      .' 

specific  gravity  of   liquids  is 

frequently  determined  by  means  of  a  hydrometer.  This 
instrument  consists  of  a  spindle-shaped  float,  which  sup- 
ports a  narrow  cylindrical  stem  bearing  a  graduated  scale 
as  represented  in  Fig.  67.  When  placed  in  a  liquid  such 
a  float  must  displace  its  own  weight  of  the  liquid  con- 
cerned, and  hence  the  point  on  the  stem  to  which  it  sinks 
must  depend  upon  its  weight,  and  the  specific  gravity 
of  the  solution.  It  can  be  calibrated  by  placing  it  in  a 
series  of  liquids  of  known  composition,  or  specific  grav-  Fig.  67.— 
ity,  and  marking  the  points  to  which  it  sinks  on  the  Hydrom- 
scale  attached  to  the  stem.  It  should  be  noted  that  eter 
equal  changes  in  the  specific  gravity  of  the  solutions  used  do  not 
shift  the  points  to  which  it  sinks  by  equal  increments.  If  the 
volume  which  it  displaces  in  a  liquid  which  has  a  specific  gravity 
of  one  is  represented  by  a  the  weight  of  the  hydrometer  must  be 
1  X  a,  and  the  volumes  displaced  when  placed  in  liquids  having 


y 


THE  USE  OF  SPECIFIC  GRAVITY  METHODS  361 

specific  gravities  of  1.01,  1.02  and  1.03  respectively  would  be 
IX  a  divided  by  these  numbers.  Since  the  three  quotients  do 
not  differ  from  each  other  by  equal  amounts,  it  is  evident  that 
each  division  on  the  scale,  corresponding  to  an  equal  difference 
in  specific  gravity,  must  have  a  slightly  different  value. 

The  sensitiveness  of  the  hydrometer,  that  is,  the  change  in  the 
point  to  which  it  sinks  resulting  from  a  given  change  in  specific 
gravity,  depends  upon  the  ratio  between  the  volume  displaced  in 
pure  water,  and  the  volume  displaced  by  a  unit  length  of  the  stem. 
Hydrometers  of  any  desired  degree  of  delicacy  can  be  constructed 
by  varying  the  relative  size  of  the  immersed  bulb,  as  compared  with 
the  diameter  of  the  stem.  Increasing  the  sensitiveness  by  this 
means  necessarily  decreases  the  range  of  specific  gravities  for  which 
it  can  be  used,  unless  the  stem  is  prolonged  to  a  point  which  not 
only  renders  the  instrument  cumbersome  and  easily  broken,  but 
necessitates  the  use  of  a  large  amount  of  liquid  for  a  determination. 
Hence  for  the  accurate  determination  of  specific  gravities  ranging 
from  0.7  to  2,  which  includes  the  usual  range  of  possibilities,  a 
number  of  instruments,  each  one  of  which  covers  a  part  of  this 
interval,  are  necessary.  A  set  of  eighteen  such  instruments,  each 
of  which  has  a  displacement  of  about  12  cm.  and  a  stem  5  mm.  in 
diameter,  makes  it  possible  to  determine  specific  gravities  over 
this  range  to  the  third  decimal  place.  In  such  a  set  the  ratio  of 
the  volume  displaced,  when  in  water,  to  the  volume  displaced 
by  that  interval  on  the  stem  which  corresponds  to  one  scale 
division  is  large,  and  the  scale  divisions  for  each  hydrometer  of 
the  set  can  be  made  uniform  without  introducing  very  large 
errors. 

One  source  of  error  in  the  use  of  hydrometers  is  the  result  of  the 
surface  tension  exerted  by  the  liquid  on  the  stem  which  tends  to 
increase  its  displacement.  As  a  consequence  a  hydrometer  will 
show  a  slightly  different  reading  when  placed  in  two  liquids  which 
have  the  same  specific  gravity  but  different  surface  tensions. 
Fortunately  these  differences  are  small. 


362  QUANTITATIVE  CHEMICAL  ANALYSIS 

The  Calibration  of  Hydrometers.  Although  hydrometers  can 
be  calibrated  to  show  specific  gravity  referred  to  water  at  4°,  or  to 
any  desired  unit  of  volume,  their  widespread  use  for  certain  techni- 
cal purposes  has  led  to  the  employment  of  a  number  of  empirical 
and  arbitrary  scales,  some  of  which  have  but  little  to  recommend 
them. 

If  the  result  ultimately  desired  is  the  percentage  composition 
of  a  solution  of  some  one  substance,  it  is  obviously  rational  to 
calibrate  the  hydrometer  used  to  read  percentages  of  that  sub- 
stance directly.  Hence  a  number  of  " direct  percentage"  hydrom- 
eters which  give  directly  the  percentage  of  alcohol  (alcoholometers), 
of  sugar  (saccharometers),  of  urea  (ureometers),  etc.,  in  aqueous 
solutions  are  in  use.  They  are  of  but  little  use,  except  for  the 
analysis  of  one  particular  kind  of  solution. 

A  number  of  the  hydrometers  first  used  in  analytical  work  were 
calibrated  so  that  the  volume  displaced  by  that  part  of  the  stem 
corresponding  to  one  scale  division  bore  a  very  simple  numerical 
relation  to  the  volume  displaced  when  in  water.  This  relation,  as 
already  shown,  is  not  a  constant  one,  unless  the  scale  divisions 
differ  by  small  values;  it  is  known  as  the  "  modulus  "  of  the  hy- 
drometer. Thus  the  modulus  of  the  Gay-Lussac  hydrometer  is 
100,  that  of  the  Balling  200,  and  that  of  the  Brix  400. 

The  Baum6  hydrometer  was  originally  calibrated  by  marking  the 
point  to  which  it  sank  in  water  0  and  in  a  10  per  cent  salt  solu- 
tion 10,  and  continuing  the  same  scale  units  down  the  stem. 
Somewhat  later  its  use  in  factories  manufacturing  sulfuric  acid 
became  general,  and  it  was  found  convenient  to  standardize  it  by 
marking  the  point  to  which  it  sank  in  sulfuric  acid,  which  had  a 
specific  gravity  of  1.842,  66.  The  two  methods  of  calibration, 
agree  with  a  fair  degree  of  approximation  only,  and  since  different 
countries  have  adopted  different  temperatures  for  the  calibration 
the  value  of  a  Baum6  degree  is  an  uncertain  quantity.  The 
Baume  hydrometer  was  also  adopted  for  use  with  liquids  lighter 
than  water  by  marking  the  point  to  which  it  sank  in  pure  water  10 


THE  USE  OF  SPECIFIC   GRAVITY  METHODS  363 

and  in  a  10  per  cent  salt  solution  0,  and  continuing  the  same 
scale  units  up  the  stem. 

The  Twaddle  hydrometer  is  calibrated  so  that  each  unit  repre- 
sents five  units  of  specific  gravity  in  the  third  decimal  place,  that 
is,  9°  Twaddle  =  1.045  Sp.  Gr. 

All  hydrometers  are  calibrated  for  use  at  some  definite  tempera- 
ture, which  should  be  specified  on  the  label  with  which  they  are 
provided.  Many  of  them  also  carry  a  small  thermometer,  which 
obviates  the  need  of  a  second  instrument. 

Calculation  of  Specific  Gravity  from  any  Hydrometer  Scale. 
The  analyst  is  often  obliged  to  calculate  specific  gravity  from  any 
of  the  arbitrary  scales  with  which  a  hydrometer  may  be  provided, 
or  to  convert  specific  gravities  into  such  scale  readings.  This  can 
be  easily  effected  if  the  modulus  of  the  instrument  concerned  is 
known.  Thus  the  modulus  of  the  American  Baume  hydrometer, 
which  is  calibrated  for  (££)  Fahrenheit,  is  145.  This  means  that 
the  volume  displaced  by  it  when  floating  in  pure  water  is  145  times 
as  great  as  the  volume  displaced  by  that  portion  of  the  stem  repre- 
senting one  scale  division.  Hence  the  volume  displaced  when 
immersed  in  a  liquid  of  specific  gravity  x  must  be  (145  -f-  x)  and 
the  change  in  the  point  to  which  it  sinks  must  be  represented  by 

145  -  (145  -H  x\     Therefore 

145        /60\ 
Degrees  Baume  (for  heavy  liquids)  =  145 —  at  f  ^ j  F°. 

The  Baume  hydrometer  for  liquids  lighter  than  water  has  a 
modulus  of  140  and  this  point  is  marked  10,  hence  the  correspond- 
ing formula  is: 

Degrees  Baume  (for  light  liquids)  = 130  at  f  ^J  F°. 

The  corresponding  formulae  for  the  Gay-Lussac,  the  Balling  and 
the  Brix  hydrometers  differ  from  that  given  above  only  in  that  the 
numbers  100,  200  and  400,  respectively  are  substituted  for  145. 

The  Westphal  Balance.  The  specific  gravity  of  liquids  can 
also  be  calculated  from  the  buoyant  effect  which  they  exert  when 


364 


QUANTITATIVE  CHEMICAL  ANALYSIS 


solid  objects  of  known  mass  and  volume  are  immersed  in  them. 
A  device  which  makes  use  of  this  principle  is  the  Westphal  balance, 
which  is  represented  in  Fig.  68.  It  consists  of  a  light  metal  beam 

suspended  horizontally.  One  end 
of  the  beam  is  provided  with  a 
pointer,  which  indicates  its  posi- 
tion with  reference  to  a  second 
pointer  attached  to  the  frame  sup- 
porting the  beam,  and  a  knob 
whose  weight  is  sufficient  to  coun- 
terbalance a  glass  plummet  sus- 
pended from  the  other  end  of  the 
beam.  If  the  plummet  is  com- 
pletely immersed  in  a  liquid  the 
latter  exerts  a  buoyant  effect, 
which  is  determined  by  the  prod- 
uct of  two  factors,  namely,  the 
specific  gravity  of  the  liquid  and 


A 


Fig.  68.— Westphal  balance 


the  volume  displaced  by  the  plummet.  This  effect  can  be  meas- 
ured by  ascertaining  what  weight  must  be  added  to  the  end  of  the 
beam  from  which  the  plummet  is  suspended  to  cause  the  beam 
to  assume  a  horizontal  position. 

If  the  unit  of  weight  employed  in  making  this  measurement  cor- 
responds exactly  to  the  buoyant  effect  which  is  found  when  the 
plummet  is  immersed  in  water,  the  weights,  measured  in  terms  of 
this  unit,  found  to  be  necessary  when  the  plummet  is  immersed  in 
any  other  liquid,  give  at  once  the  specific  gravity  of  that  liquid. 
Hence  the  apparatus  is  provided  with  a  special  set  of  weights,  made 
to  take  the  form  of  riders,  which  bear  simple  relations  to  the  volume 
and  weight  of  the  plummet.  Since  that  half  of  the  beam  from 
which  the  plummet  is  suspended  is  divided  into  ten  equal  divisions, 
only  five  such  weights,  two  of  unit  value  and  one  each  of  0.1,  0.01 
and  0.001  of  this  value  are  needed  to  counterbalance  the  buoyant 
effect  of  any  liquid  mixture,  whose  specific  gravity  ranges  from 
0.001  to  2.999. 


THE  USE  OF  SPECIFIC  GRAVITY  METHODS  365 

The  specific  gravity  of  liquids  can  be  determined  with  this 
instrument  in  a  few  minutes,  often  with  an  error  not  exceeding 
0.0005.  The  error  involved  increases  rapidly  with  the  viscosity 
of  the  liquid  concerned,  owing  to  its  action  on  the  movements  of 
the  plummet,  which  prevents  the  beam  from  attaining  its  normal 
position. 

Analysis  of  Solid  Mixtures.  The  specific  volume  of  a  solid 
mixture  is  a  simple  additive  function  of  the  specific  volumes  of 
its  components  if  the  mixture  represents  a  simple  conglomerate. 
This  statement  is  also  approximately  true  of  mixtures  which  con- 
sist of  solid  solutions.  Altho  theoretically  this  principle  is  appli- 
cable to  the  analysis  of  all  heavy  mixtures  of  either  of  these  classes, 
the  number  of  cases  in  which  it  can  be  used  with  a  sufficient  degree 
of  certainty  and  accuracy  is  small.  It  is  often  difficult  to  ascer- 
tain whether  small  amounts  of  other  components  are  not  also 
present;  this  is  especially  true  of  naturally  occurring  substances, 
which  often  contain  solid  or  liquid  inclusions,  which  can  only  be 
recognized  by  making  a  thin  section  and  examining  it  with  a  com- 
pound microscope.  The  specific  volume  of  many  solids  is  affected 
by  the  rate  at  which  they  have  been  cooled  during  solidification, 
that  of  other  solids,  especially  metals  and  alloys,  is  affected  by 
mechanical  deformation,  such  as  hammering  or  rolling.  Still 
others  can  exist  in  two  or  more  allotropic  forms  whose  specific 
volumes  differ,  and  which  may  persist  above  or  below  the  normal 
temperature  limits  at  which  they  are  stable.  The  most  important 
applications  of  the  method  are  in  determining  the  relative  amounts 
of  two  minerals  in  a  rock  formation  and  in  the  analysis  of  certain 
simple  alloys. 

Analysis  of  Liquid  Mixtures.  The  most  widely  used  of  all 
physico-chemical  methods  are  determinations  of  the  percentage 
composition  of  aqueous  solutions  by  means  of  specific  gravity 
determinations.  They  cannot  be  used  where  the  liquid  mixture 
contains  appreciable  amounts  of  a  third  constituent,  for  every 
component  of  such  mixtures  has  some  effect  upon  its  specific 


366  QUANTITATIVE  CHEMICAL  ANALYSIS 

gravity.  Even  when  two  components  only  are  present  the  specific 
gravity  of  such  mixtures  rarely  bears  a  simple  relation  to  those  of 
the  pure  components,  at  least  over  a  wide  range  of  concentrations. 
The  simplicity  and  accuracy  with  which  specific  gravity  determi- 
nations can  be  made  has  led  to  the  preparation  of  a  large  number 
of  tables  which  give  this  relation  for  a  great  variety  of  such  mix- 
tures, and  has  resulted  in  their  extended  use  in  many  kinds  of 
technical  work. 

II.   ANALYSIS  OF  A  LEAD-TIN  ALLOY 

Facts  Upon  Which  the  Method  is  Based.  These  metals  are 
not  appreciably  soluble  in  each  other  in  the  solid  state,  nor  do 
they  form  compounds  with  each  other.  The  specific  gravity  of 
the  ordinary  tetragonal  modification  of  tin,  which  is  stable  between 
18°  and  161°,  is  7.29,  and  the  specific  volume  is  therefore  0.1371. 
The  specific  gravity  of  lead  is  11.35  and  its  specific  volume  is  there- 
fore 0.08811.  These  values  are  affected  but  slightly  by  changes 
of  several  degrees  in  temperature. 

If  the  specific  volumes  of  these  alloys  are  linear  functions  of 
their  percentage  composition  it  should  be  possible  to  analyze  any 
such  alloy  whose  specific  volume  V  is  known  by  use  of  the  formula 

_  100  (V  -  0.08811), 
=  0.1371  -  0.08811  ' 

where  x  is  the  percentage  of  tin  present  by  volume. 

Experimental  work  has  shown  that  this  relation  is  only  approxi- 
mately correct;  the  departures  found,  which  are  sometimes  posi- 
tive and  sometimes  negative,  do  not  exceed  nine-tenths  of  1  per 
cent,  and  the  method  is  used  where  speed  is  more  important  than 
accuracy. 

Outline  of  the  Method  of  Procedure.  Select  a  lump  of  the 
alloy  which  weighs  from  10  to  15  gm.  and  weigh  accurately.  Wrap 
one  end  of  a  piece  of  aluminum  wire  around  the  lump  so  that  it  can 
be  suspended  by  it.  Place  the  specimen  in  a  small  beaker  con- 


THE  USE  OF  SPECIFIC  GRAVITY  METHODS  367 

taining  distilled  water,  heat  the  latter  to  the  boiling  point  and 
boil  for  about  3  minutes.  Allow  to  cool  to  a  temperature  of  20° 
without  removing  the  sample,  then  support  the  beaker  on  the 
wooden  bridge  with  which  the  balance  is  supplied  and  suspend 
the  specimen  from  the  hook  attached  to  the  balance  beam  as 
shown  in  Fig.  W?  Determine  the  weight  necessary  to  counter- 
balance the  specimen.  Remove  the  specimen  from  the  support- 
ing wire  and  determine  the  weight  necessary  to  counterbalance 
the  latter  when  immersed  to  the  point  previously  reached  and 
subtract  the  result  from  the  weight  previously  found. 

Calculate  the  specific  gravity  from  the  formula  given  on  page 
358,  assuming  G  =  1,  the  volume  percentage  of  tin  from  the  for- 
mula given  in  the  preceding  paragraph,  and  finally  the  weight 
percentage  of  tin. 

III.   DETERMINATION  OF  SULFURIC  ACID  IN  A  COMMERCIAL 

SAMPLE 

Facts  Upon  Which  the  Method  is  Based.  The  relation  be- 
tween the  percentage  composition  and  the  specific  gravity  of 
aqueous  solutions  of  sulfuric  acid  is  represented  by  a  curve,  which 
differs  but  slightly  from  a  straight  line  over  the  interval  between 
zero  and  80  per  cent.  For  much  of  this  interval  the  percentage 
can  be  calculated  from  the  specific  gravity  by  simple  formulae; 
between  66  and  81  per  cent  it  can  be  calculated  with  great  accu- 
racy by  multiplying  by  86  -and  subtracting  68.82.  Beyond  80 
per  cent  the  specific  gravity  increases  at  a  rate  which  decreases 
continuously  and  beyond  97  per  cent  the  specific  gravity  begins 
to  decrease.  The  amounts  of  impurities  present  in  commercial 
samples  are  usually  too  small  to  affect  its  specific  gravity 
greatly. 

Outline  of  Method  of  Procedure.     Procure  a  set  of  hydrom- 

(15°\ 
40- JC-     Fil1 

a  clean,  dry,  glass  cylinder,  whose  inner  diameter  is  at  least  twice 


368  QUANTITATIVE  CHEMICAL  ANALYSIS 

that  of  the  hydrometers,  about  two-thirds  full  of  the  sample  and 
bring  to  a  temperature  of  15°  by  immersing  in  warm  or  cold  water 
and  stirring  with  a  thermometer.  Choose  the  proper  hydrometer 
of  the  set,  which  may  necessitate  several  preliminary  experiments, 
and  allow  it  to  sink  gradually  in  the  acid  but  avoid  allowing  any 
of  the  acid  to  touch  the  hydrometer  above  the  point  to  which  it 
finally  sinks,  and  keep  it  in  the  center  of  the  cylinder.  Place  the 
eye  slightly  below  the  level  of  the  acid  and  read  the  point  at  which 
the  plane  representing  the  surface  of  the  liquid  intersects  the  scale 
of  the  hydrometer. 

Remove  the  hydrometer  from  the  cylinder,  rinse  it  off  under  the 
tap  and  wipe  dry.  Return  the  acid  to  the  sample  bottle,  rinse 
out  the  cylinder  and  wipe  it  dry.  Calculate  the  percentage  of 
sulfuric  acid  present  by  use  of  the  table  on  pages  383-384. 

IV.   DETERMINATION  OF  THE  SPECIFIC  GRAVITY  OF 
CRUDE  PETROLEUM 

Facts  Upon  Which  the  Determination  is  Based.  In  the  com- 
mercial evaluation  of  crude  petroleum  much  importance  is  at- 
tached to  its  specific  gravity.  This  is  a  consequence  of  the  fact 
that  the  more  valuable  saturated  hydrocarbons  of  low  atomic 
weight  are  much  lighter  than  the  less  valuable  olefines,  napthenes, 
and  asphalt,  and  hence  the  specific  gravity  of  the  sample  indicates 
roughly  the  value  of  the  products  which  can  be  obtained  from  it 
when  refined. 

Thru  long-established  custom  the  Baume  hydrometer,  for  liquids 
lighter  than  water,  is  generally  used  in  America  in  the  petroleum 
industry  in  expressing  the  gravity  of  both  the  crude  oil  and  the 
various  products,  gasolenes,  kerosenes,  lubricating  oils,  which  are 
prepared  from  it.  The  high  viscosity  of  many  samples  of  crude 
oil,  and  its  opacity,  often  make  an  accurate  determination  of  the 
specific  gravity  difficult.  The  effect  of  temperature  on  the  specific 
gravity  is  very  large,  and  all  determinations  should  be  made  at 
60°  F.  (15.56°  C.)  for  which  the  hydrometer  is  calibrated. 


THE  USE  OF  SPECIFIC  GRAVITY  METHODS  369 

Outline  of  Method  of  Procedure.  Test  the  temperature  of 
the  sample  and  if  necessary  place  the  bottle  containing  it  in  a  vessel 
of  warm  or  cold  water,  and  stir  the  petroleum  with  a  thermometer 
until  the  latter  registers  15.56°  C.  Pour  a  sufficient  amount  of  the 
sample  into  a  clean,  dry,  glass  cylinder,  whose  diameter  is  at  least 
twice  that  of  the  hydrometer  to  be  used,  and  fill  it  about  two-thirds 
full.  Allow  the  hydrometer,  which  should  be  clean  and  dry,  to 
sink  slowly  in  the  petroleum  until  it  comes  to  rest.  Place  the  eye 
on  a  level  with  the  liquid  and  sight  across  this  level  to  the  stem  of 
the  hydrometer,  that  is,  endeavor  to  read  the  point  corresponding 
to  the  level  of  the  liquid,  not  the  point  to  which  some  of  the  liquid 
is  drawn  on  the  stem  by  surface  tension.  Report  the  result  in 
Baume  degrees  and  absolute  specific  gravity. 

V.  QUESTIONS  AND  PROBLEMS.    SERIES  25 

1.  Calculate  the  modulus  of  a  hydrometer  which  sank  to  a  point  marked 
zero  in  water  and  to  a  point  marked  50  in  a  solution  containing  seventy  per 
cent  of  sulfuric  acid. 

2.  Specify  dimensions  for  a  hydrometer  which  could  be  used  to  determine 
specific  gravities  ranging  from  1.4000  to  1.4200ty  and  for  which  each  unit 
in  the  fourth  decimal  place  corresponds  to  1  mm.  on  the  scale. 

3.  A  sample  of  hydrochloric  acid  gave  a  reading  of  16  on  an  American 
Baume  hydrometer.     What  would  be  the  reading  if  a  Brix  hydrometer  was 
placed  in  it? 

4.  What  volume  of  sulfuric  acid  of  specific  gravity  1.8  must  be  added  to 
100  cc.  of  65  per  cent  acid  to  make  it  75  per  cent? 

5.  If  a  Twaddle  hydrometer  is  placed  in  80  per  cent  sulfuric  acid,  what 
would  it  read? 

6.  Plot  a  curve  showing  the  relation  of  specific  gravity  to  percentage 
composition  for  the  lead- tin  alloys. 

7.  Indicate  the  probable  form  of  the  curve  representing  the  relation  of 
specific  gravity  to  percentage  composition  of  lead-tin  alloys  if  it  is  assumed 
that  a  compound  of  the  formula  PbSn2  is  formed. 

8.  A  mixture  of  methyl  and  ethyl  alcohol  has  a  specific  gravity  of  0.85564 
at  20°  and  a  refraction  index  of  60  on  a  Zeiss  immersion  refractometer.     What 
per  cents  of  methyl  and  ethyl  alcohol  are  present? 


CHAPTER  L 

COLORIMETRIC   PROCESSES 
I.   GENERAL  FEATURES  OF  COLORIMETRIC  PROCESSES 

Principle  Involved.  Certain  substances,  when  dissolved  in  an 
appropriate  solvent,  yield  solutions  which  show  a  characteristic 
color  absorption  when  viewed  by  transmitted  light,  and  it  becomes 
possible  to  determine  the  concentration  of  such  solutions  by  com- 
paring the  intensity  of  this  absorption  with  that  of  a  solution 
containing  a  known  concentration  of  the  substance  concerned.  A 
large  number  of  quantitative  processes  are  based  upon  this  prin- 
ciple and  are  designated  as  "  colorimetric "  processes.  They 
depend  upon  the  measurement  of  a  physical  property,  but  the 
property  here  concerned  is  a  complex  one,  and  cannot  be  deter- 
mined and  expressed  numerically  except  by  reference  to  a  purely 
empirical  standard,  that  is,  a  second  solution  of  known  concentra- 
tion. As  a  consequence  the  methods  used  in  carrying  out  such 
determinations  closely  resemble  those  used  in  volumetric  processes; 
hence  they  are  frequently  classed  as  a  separate  group,  rather  than 
with  the  other  physico-chemical  processes. 

The  intensity  of  the  shade  of  color  transmitted  by  two  solutions 
of  the  same  solute  in  the  same  solvent  depends  upon  the  concen- 
trations of  the  two  solutions  and  the  thickness  of  the  two  layers 
compared.  Since  the  absorption  may  be  due  to  the  presence  of 
either  the  undissociated  molecule,  or  of  one  or  more  of  the  ions  into 
which  it  dissociates,  it  is  affected  by  all  of  the  conditions  which 
affect  the  dissociation  of  electrolytes.  If  the  concentrations  are 
such  that  the  dissociation  is  complete,  and  if  other  changes,  such 
as  hydration,  do  not  take  place  the  intensity  of  absorption  will  be 
directly  proportional  to  the  concentration,  but  this  is  rarely  true. 

370 


COLORIMETRIC  PROCESSES  371 

Methods  of  Making  Colorimetric  Determinations.  All  color- 
imetric  processes  involve  varying  the  thickness,  the  volume,  or 
the  concentration  of  either  the  standard  or  the  unknown  solution 
until  the  two  show  an  absorption  of  equal  intensity;  hence  three 
types  of  method  are  possible. 

In  the  first  the  volumes  and  concentrations  remain  constant, 
and  the  ratio  between  the  thickness  of  the  layers  of  the  two  solu- 
tions at  which  the  absorption  is  equally  intense,  is  measured.  This 
type  of  method  assumes  that  the  intensity  of  absorption  is  directly 
proportional  to  the  concentration,  which,  as  shown  in  the  preceding 
paragraph,  is  not  necessarily  correct.  This  type  of  method  is 
but  rarely  used  in  actual  practice,  except  for  the  purpose  of  making 
the  final  comparison  between  two  solutions  which  possess  approxi- 
mately the  same  concentration,  that  is,  it  is  frequently  necessary 
to  combine  it  with  methods  of  the  second  or  third  type. 

In  the  second  type  of  method  the  thicknesses  observed  remain 
constant,  and  the  ratio  of  the  volumes  of  the  two  solutions  at 
which  the  absorption  is  equally  intense  is  measured. 

In  the  third  type  the  thicknesses  observed  and  the  volumes  are 
kept  constant,  and  the  concentration  of  the  standard  solution  is 
increased  until  it  shows  an  absorption  equal  in  intensity  to  that 
of  the  unknown  solution. 

Colorimeters.  The  relation  between  the  colorific  intensities 
of  two  solutions  is  determined  by  means  of  a  "  colorimeter. "  An 
inexpensive  and  for  most  purposes  sufficiently  accurate  form  of 
this  instrument  is  that  of  Wolff,  a  diagram  of  which  is  represented 
in  Fig.  69.  It  consists  of  two  glass  cylinders  A  and  B,  which  are 
accurately  calibrated,  and  provided  with  glass  stopcocks  by  means 
of  which  the  solutions  contained  by  them  can  be  drawn  off;  they 
are  supported  in  a  frame  which  holds  them  in  the  same  position 
with  respect  to  the  mirror  M.  The  light  reflected  from  the  mirror 
passes  thru  the  solutions  in  the  two  cylinders  and  is  combined  by 
an  optical  device  in  such  a  manner  that  the  two  halves  of  the  eye- 
piece are  illuminated  by  light  which  has  passed  thru  the  two 


372 


QUANTITATIVE  CHEMICAL  ANALYSIS 


cylinders.  The  cylinders  are  enclosed  in  a  case  which  eliminates 
the  disturbing  action  of  light  from  other  sources.  In  using  this 
instrument  the  more  concentrated  solution  is  diluted  until  the 
colorific  absorptions  are  nearly  equal,  and  the  exact  relation  of 


llf 

1 

h 

m 
1 

A- 

r± 
^ 

i 

i 

L 

Hi 

_B 

t 
™"~"  _ 

m 

P> 

-M 

junta 

Fig.  69.  — Wolff's  Colorimeter          Fig.  70.  —  Stammar's  Colorimeter 

the  two  absorptions  determined  by  reducing  the  thickness  of  the 
layer  of  the  more  concentrated  solution  until  the  two  halves  of 
the  field  of  view  show  equal  illumination. 

A  more  expensive  instrument  is  that  of  Stammar,  a  diagram  of 
which  is  represented  in  Fig.  70.  In  this  apparatus  one  of  the  two 
solutions  is  retained  in  a  tube,  which  can  be  closed  at  both  ends 
by  plates  of  glass,  held  in  position  by  means  of  rings  which  can 
be  screwed  onto  the  end  of  the  tube;  the  other  solution  is  retained 


COLORIMETRIC   PROCESSES  373 

in  a  jar,  which  can  be  raised  or  lowered  with  respect  to  the  base 
of  the  instrument  by  changing  the  position  of  the  clamp  which 
supports  it.  A  glass  piston,  the  end  of  which  is  flat  and  polished, 
projects  into  this  jar,  and  by  varying  the  position  of  the  jar  the 
thickness  of  the  layer  of  liquid  between  the  bottom  of  the  piston 
and  the  bottom  of  the  jar  can  be  varied.  The  ratio  of  the  thick- 
nesses of  the  two  solutions  under  observation  can  then  be  read  off 
directly  from  the  index  fastened  to  the  frame  bearing  the  jar,  with 
respect  to  the  frame  of  the  apparatus;  its  other  features  are 
essentially  the  same  as  those  of  the  Wolff  colorimeter. 

Color  Comparison  Tubes.  The  second  method  of  making  a 
colorimetric  determination  is  usually  carried  out  in  long  narrow 
tubes,  in  one  of  which  the  more  concentrated  solution  is  diluted 
and  mixed,  until  the  colorific  intensities  are  equal.  The  actual 
comparison  is  made  in  a  box  with  darkened  sides  open  at  both  ends; 
when  in  use  one  end  is  directed  against  the  source  of  light  employed, 
the  other  being  the  point  of  observation. 

Nessler  Cylinders.  The  third  method  is  usually  carried  out 
in  "  Nessler  tubes/7  They  are  made  of  clear,  colorless  glass,  of  an 
equal  and  uniform  diameter  with  flat  smooth  bottoms.  They 
are  provided  with  marks  corresponding  to  volumes  of  50,  100,  150 
or  200  cc.  In  using  them  the  solution  whose  concentration  is  to 
be  estimated  is  diluted  to  one  of  the  four  standard  volumes,  and  a 
standard  prepared  in  a  companion  cylinder,  by  adding  to  it  a 
sufficient  amount  of  an  accurately  standardized  solution  of  the 
substance  which  is  being  estimated,  to  give  at  the  same  volume,  an 
equal  color  absorption.  The  amount  of  substance  present  is  then 
calculated  from  the  volume  of  the  standard  solution  used  and  its 
concentration. 

Where  a  large  number  of  such  determinations  are  being  made, 
or  where  they  are  part  of  a  daily  routine,  it  is  desirable  to  prepare 
a  permanent  series  of  color  standards  of  a  sufficiently  wide  range 
of  concentrations.  Where  these  are  prepared  it  is  preferable  to 
substitute  a  bottle  of  uniform  diameter  for  the  cylindrical  tubes. 


374  QUANTITATIVE  CHEMICAL  ANALYSIS 

Limitations  of  Colorimetric  Methods.  The  actual  percentage 
error  involved  in  making  a  colorimetric  comparison  is  rather  large, 
unless  an  elaborate  colorimeter  is  used  and  especially  favorable 
conditions  can  be  maintained.  Very  slight  differences  in  the 
character  of  the  light  absorbed  by  the  two  solutions,  which  may 
result  from  the  presence  of  small  amounts  of  other  substances  in 
the  sample  being  analyzed,  increase  the  percentage  error  materi- 
ally, altho  in  such  instances  the  effort  is  usually  made  to  avoid  the 
difficulty  by  introducing  approximately  equal  amounts  of  these 
substances  in  the  prepared  standards.  Slight  differences  in  the 
thickness  or  absorption  capacity  of  the  glass  vessels  used  to  retain 
the  solutions  exercise  a  disturbing  influence;  also,  the  personal 
qualifications  of  the  analyst,  that  is,  his  ability  to  distinguish  color 
shades,  has  an  unusually  large  effect  upon  the  results  obtained. 

Experience  proves  that  with  most  colorific  substances  there  is 
a  certain  range  of  concentrations  at  which  the  color  shades  change 
most  decidedly  with  the  concentration,  and  the  percentage  error  of 
the  comparison  may  be  large  unless  made  within  this  range.  The 
kind  of  light  used  in  making  the  comparison  is  also  a  factor; 
usually  pure  white  light,  such  as  is  reflected  from  a  white  opaque, 
or  translucent  mirror,  gives  the  best  results. 

With  most  of  the  colorimetric  processes  in  common  use  the  final 
comparison  must  be  made  with  solutions  containing  a  very  small 
concentration  of  the  colored  compound,  and  the  percentage  error 
of  the  process  is  sufficiently  small  only  when  the  total  amount  of 
the  substance  which  is  being  estimated  is  small.  Hence  colori- 
metric processes  are  in  general  poorly  adapted  to  the  analysis  of 
substances  containing  large  percentages  of  the  element  or  com- 
pound concerned,  for  altho  the  amount  of  substances  actually 
determined  may  be  made  small  by  using  a  very  small  weight  of  the 
sample,  or  by  taking  a  small  fraction  of  the  solution  first  prepared, 
the  error  concerned  in  the  final  comparison  is  then  multiplied 
sufficiently  to  give  a  large  departure  in  the  final  result. 

On  the  other  hand,  colorimetric  processes  are  peculiarly  adapted 


COLORIMETRIC   PROCESSES  375 

to  the  determination  of  small  percentages  of  many  elements  and 
compounds.  Usually  previous  separation  of  the  constituent 
which  is  being  determined  is  unnecessary,  and  in  many  cases 
amounts  which  are  entirely  too  small  to  be  estimated  by  any  other 
class  of  methods  can  be  determined  colorimetrically  with  a  satis- 
factory percentage  accuracy.  A  very  large  number  of  such  proc- 
esses have  been  elaborated  and  are  in  general  use.* 

II.  DETERMINATION  OF  MANGANESE  IN  CAST  IRON  AND  STEEL 
Colorific  Power  of  Permanganates.     Solutions  which  contain 

the  permanganic  ion  MnO4  possess  a  deep  red  or  pink  color,  the 
intensity  of  which  is  approximately  proportional  to  the  concen- 
tration; hence  the  amount  of  manganese  present  in  this  form  can 
be  accurately  determined  by  comparing  the  color  of  the  unknown 
with  that  of  a  standard  permanganate  solution.  If  the  compari- 
son is  made  in  tubes  containing  a  layer  of  solution  100  mm.  in 
thickness  the  best  results  are  obtained  when  the  concentration  is 
in  the  neighborhood  of  10  mg.  of  manganese  per  liter.  As  the 
permanganic  ion  is  readily  reduced  by  organic  matter  or  even  by 
light  the  solutions  compared  fade  appreciably  on  long  standing, 
unless  oxidizing  agents  of  sufficient  strength  are  also  present. 

The  Formation  of  Permanganates.  The  complete  conver- 
sion of  the  manganous  ion  into  the  permanganic  ion  can  be  effected 
by  certain  oxidizing  agents,  but  only  in  the  absence  of  hydro- 
chloric acid,  and  in  the  presence  of  a  large  concentration  of  nitric 
acid.  Lead  peroxide  and  sodium  bismuthate  are  often  employed 
for  this  purpose,  but  a  more  convenient  reagent  to  use  is  ammonium 
or  potassium  persulfate,  the  action  of  which  can  be  represented 
by  the  expression: 
5  (NH4)2S208  +  2  Mn(N03)  +  8  H20  ->  5  (NH4)2S04  +  2  HMnO4 

+  5H2S04  +  4NH03. 

The  speed  of  this  reaction  under  ordinary  conditions  is  not  great 
*  See  Schreiner,  Jour,  of  the  Am.  Chem.  Soc.,  27,  1192  (1903). 


376  QUANTITATIVE   CHEMICAL  ANALYSIS 

but  in  the  presence  of  a  silver  salt  and  at  a  temperature  above  70° 
it  progresses  rapidly.  The  function  of  the  silver  salt  seems  to  be 
that  of  a  catalyzer;  in  its  absence  some  of  the  manganese  may 
separate  as  the  dioxide. 

Application  of  the  Method.  This  method  is  especially  useful 
in  the  estimation  of  the  small  amounts  of  manganese  found  in  the 
commercial  alloys  of  iron  and  in  iron  ores.  In  applying  the  method 
to  such  determinations  the  error  resulting  from  the  color  imparted 
to  the  solution  by  the  ferric  ions  present  and  that  due  to  the  color 
which  results  from  the  partial  oxidation  of  the  carbon  of  iron  car- 
bide by  the  nitric  acid  usually  employed  to  dissolve  such  alloys 
must  be  considered.  The  colorific  power  of  the  ferric  ion,  espe- 
cially in  a  nitric  acid  solution,  and  at  ordinary  temperatures,  is 
extremely  small  as  compared  with  that  of  the  permanganic  ion, 
and  even  though  the  percentage  of  iron  is  one  hundred  times  as 
great  as  that  of  manganese,  it  modifies  to  a  slight  degree  only  the 
color  resulting  from  the  permanganate  ion.  The  color  due  to 
carbon,  especially  in  the  analysis  of  steels  containing  a  large  per- 
centage of  carbon,  is  a  more  important  item,  but  the  difficulty  is 
eliminated  if  the  precaution  is  taken  to  treat  the  solution  with  an 
excess  of  some  oxidizing  agent,  such  as  ammonium  persulfate, 
which  slowly  oxidizes  the  carbon  to  carbon  dioxide.  Actual 
experience  with  the  process  shows  that  it  is  scarcely  possible  to 
prepare  a  solution  of  the  sample  containing  all  of  the  manganese 
as  permanganate,  which  possesses  exactly  the  same  color  shade  as 
a  pure  solution  of  a  soluble  permanganate.  It  is  preferable,  there- 
fore, to  prepare  the  color  standard  used  from  an  alloy  or  ore,  whose 
manganese  content  has  been  previously  determined  with  great 
accuracy,  preferably  from  a  sample  in  which  the  ratio  of  iron  to 
manganese  is  approximately  the  same  as  that  in  the  sample  under 
consideration. 

In  the  analysis  of  samples  of  gray  cast  iron,  a  fine  black  residue 
representing  carbon  and  silicon,  which  remains  insoluble  also 
interferes  with  the  color  comparison,  and  makes  filtration  neces- 


COLORIMETRIC  PROCESSES  377 

sary.  The  entire  process  is  a  simple  one  and  under  favorable 
conditions  a  determination  can  be  made  within  one  half  hour. 

Outline  of  Method  of  Procedure.  Weigh  out  0.2  gm.  of  the 
standard,  the  manganese  content  of  which  is  accurately  known, 
and  an  equal  amount  of  the  unknown  sample  and  place  in  test 
tubes,  which  have  a  capacity  of  70  cc.  Add  to  both  tubes 
10  cc.  of  dilute  nitric  acid,  and  warm  both  in  a  water  bath  until 
complete  decomposition  has  been  effected  and  oxides  of  nitrogen 
are  no  longer  evolved,  then  add  about  one-half  gram  of  ammonium 
persulfate  and  continue  heating  with  occasional  shaking  until 
oxygen  is  no  longer  given  off.  If  a  large  amount  of  carbon  remains 
in  either  tube,  that  is,  if  either  sample  contains  much  graphitic 
carbon,  filter  through  a  small  7  cm.  filter  into  a  second  test  tube 
and  wash  the  filter  with  about  10  cc.  of  water.  Next  dilute  both 
solutions  to  a  volume  of  20  cc.  add  JO  cc.  of  reagent  silver  nitrate 
solution  and  then  1  gm.  of  ammonium  persulfate.  Place  both 
tubes  in  the  water  bath  and  allow  to  remain  with  occasional 
shaking  until  the  maximum  amount  of  red  color  is  developed, 
which  should  not  require  more  than  five  minutes. 

Cool  both  tubes  by  means  of  a  stream  from  the  water  tap, 
transfer  to  200  cc.  graduated  flasks  and  dilute  both  to  exactly 
that  volume.  If  one  of  the  two  solutions  shows  a  much  greater 
color  absorption  than  the  other  dilute  the  former  to  exactly  300, 
400  or  500  cc.,  that  is,  until  the  color  absorption  of  the  two  solu- 
tions does  not  differ  greatly. 

Transfer  a  portion  of  the  solution  which  has  the  less  intense  color 
to  a  color  comparison  cylinder,  preferably  of  the  Stammer  or  Wolff 
type,  using  sufficient  to  give  a  layer  which  is  from  100  to  150  nun. 
in  thickness;  transfer  a  somewhat  smaller  amount  of  the  second 
solution  to  the  other  cylinder  of  the  apparatus.  Adjust  the  arm 
which  sustains  the  second  cylinder,  if  a  Stammar  colorimeter  is 
used,  or  the  thickness  of  the  solution  in  the  second  cylinder,  if  a 
Wolff  apparatus  is  used,  until  no  difference  can  be  detected  in  the 
amount  of  absorption  in  the  two  cylinders  and  ascertain  the  com- 


378  QUANTITATIVE   CHEMICAL   ANALYSIS 

parative  depths  of  solution  observed.  Repeat  the  adjustment 
and  observation  at  least  twice  more  and  take  the  mean  of  the  three 
as  the  final  correct  result. 

Calculate  the  percentage  of  manganese  present  from  the  per  cent 
of  Mn  in  the  standard  sample;  the  volumes  to  which  the  two 
solutions  were  diluted  and  depths  of  the  layers  which  gave  equal 
color  absorptions. 

III.   DETERMINATION  OF  COPPER  IN  A  COPPER  SLAG 

Properties  of  the  Cupric-Ammonium  Ion.  Whenever  an  ex- 
cess of  ammonium  hydroxide  is  added  to  a  solution  containing 
cupric  salt  an  intense  blue  color  is  produced,  owing  to  the  forma- 
tion of  the  cupric  ammonium  ion.  This  ion  is  usually  represented 

+      +  +      + 

by  the  formula  Cu(NH3)4,  but  ions  having  the  formulas  Cu(NH3)5 

and  Cu(NH3)6  are  believed  to  be  present  in  small  amounts  in  such 
solutions.  Its  colorific  power  can  be  inferred  from  the  fact  that 
1  mg.  of  copper  in  this  form  imparts  a  color  to  100  cc.  of  water, 
which  can  be  recognized  in  layers  of  solution  8  cm.  in  thickness. 
The  intensity  of  the  color  increases  with  increasing  concentration 
at  a  fairly  uniform  rate  up  to  values  some  twenty  times  as  great 
as  the  minimum  given. 

Apparently  the  intensity  of  the  color  of  such  solutions  is  affected 
to  some  extent  by  the  nature  of  the  anions,  and  the  concentration 
of  the  ammonium  salts  and  ammonium  hydroxide  present  in  the 
solution;  hence  all  comparisons  should  be  made  with  solutions  of 
approximately  the  same  composition.  It  has  also  been  found  that 
the  colorific  intensity  of  such  solutions  remains  unchanged,  even 
after  long  standing,  if  it  contains  S04  rather  than  NOs  ions.  In 
using  the  method  it  is  customary  to  prepare  a  series  of  color 
standards  with  which  the  solution  to  be  tested  is  compared. 

Decomposition  of  Copper  Slags.  Copper  slags  which  have 
been  "  chilled/'  that  is,  suddenly  cooled  by  dropping  the  molten 


COLORIMETRIC  PROCESSES  379 

slag  from  the  furnace  into  cold  water,  and  which  have  been  finely 
ground,  can  be  readily  and  completely  decomposed  by  strong 
hydrochloric  acid.  If  the  sample  is  stirred  constantly  'during  the 
decomposition,  and  diluted  as  soon  as  this  has  been  completed, 
it  is  possible  to  avoid  the  separation  of  gelatinous  silica;  further, 
all  the  copper  can  be  precipitated  from  this  diluted  solution  by 
means  of  hydrogen  sulfide,  and  all  of  it  separated  from  the  iron, 
and  other  elements  normally  present.  If  the  proper  conditions 
are  not  complied  with  in  making  the  decomposition  some  of  the 
silica  will  separate  in  gelatinous  form,  and  it  then  becomes  neces- 
sary to  dehydrate  and  separate  all  of  the  silica  before  the  copper 
can  be  separated,  which  greatly  increases  the  time  required. 

The  percentage  of  copper  normally  present  in  blast  furnace 
slags  should  not  exceed  0.3  per  cent;  " converter"  slags  may  con- 
tain as  much  as  2.5  per  cent.  The  colorimetric  method  is  especi- 
ally adapted  to  the  analysis  of  such  products,  owing  to  its  simplicity 
and  speed;  its  accuracy  is  not  sufficient  to  make  it  a  satisfactory 
method  for  the  evaluation  of  copper  ores. 

Preparation  of  a  Series  of  Color  Standards.  Weigh  out  ex- 
actly 0.2  gm.  of  pure  copper  foil,  place  in  a  200  cc.  flask,  add  20  ec. 
of  dilute  nitric  acid,  warm  gently  until  the  copper  is  dissolved, 
then  evaporate  to  about  10  cc.  Dilute  the  solution  to  50  cc., 
transfer  to  a  graduated  liter  flask,  add  200  cc.  of  reagent  ammonium 
hydroxide,  allow  to  cool  and  dilute  to  the  mark  in  the  flask. 
Procure  and  carefully  clean  six  150  cc.  bottles  made  from  clear, 
colorless  glass,  whose  cross  section  is  represented  by  a  square.  To 
the  first  of  these  add  exactly  50  cc.  .of  the  copper  solution  and 
dilute  to  exactly  100  cc.  with  a  mixture  of  one  volume  of  ammonium 
hydroxide  and  three  of  water.  To  the  second  add  40  cc.  of  copper 
solution  and  sufficient  diluted  ammonium  hydroxide  to  make  a 
volume  of  100  cc.  and  in  the  preparation  of  each  succeeding 
standard  reduce  the  volume  of  the  copper  solution  by  10  cc.  and 
increase  the  volume  of  diluted  ammonium  hydroxide  by  the  same 
amount. 


380  QUANTITATIVE  CHEMICAL  ANALYSIS 

Outline  of  Method  of  Procedure.  Crush  the  sample  until  fim 
enough  to  pass  thru  a  100-mesh  sieve.  Weigh  out  2  gm.  into  a 
200  cc.  beaker,  add  10  cc.  of  water  and  stir  until  all  of  the  particles 
are  moistened,  then  add  8  cc.  of  concentrated  hydrochloric  acic 
and  stir  continuously  for  5  minutes,  or  until  the  undissolvec 
residue  is  black  and  flocculent,  and  remains  for  the  most  parl 
suspended  in  the  liquid. 

Add  to  the  mixture,  without  further  delay,  70  cc.  of  hydroger 
sulfide  water,  or  add  that  amount  of  water  and  saturate  with  the 
gas.  Warm  for  a  few  minutes  or  until  the  precipitated  coppei 
sulfide  coagulates,  then  filter  thru  a  Witt  filter  and  wash  twic^ 
with  10  cc.  of  water. 

Transfer  the  asbestos  filter  and  adhering  precipitate  to  the  beakei 
used  for  the  decomposition,  rinse  out  the  filter  tube  with  5  cc.  o] 
concentrated  nitric  acid,  receiving  the  rinsings  in  the  beaker,  and 
warm  the  mixture  until  all  of  the  copper  sulfide  present  has  been 
brought  into  solution.  Add  to  the  mixture  30  cc.  of  reagenl 
ammonium  hydroxide,  heat  to  about  60°  and  filter  thru  a  Witl 
filter,  which  has  been  wrell  washed  from  adhering  fibers,  and  wash 
twice  with  10  cc.  portions  of  dilute  ammonium  hydroxide. 

Transfer  the  filtrate  to  a  bottle  similar  to  those  used  for  the 
preparation  of  the  color  standards.  Compare  the  color  of  this 
bottle  with  that  of  the  standards  and  ascertain  to  which  one  it  is 
equivalent.  Calculate  the  percentage  of  copper  present  from  the 
weight  of  copper  in  the  standard  bottle  finally  chosen  and  the 
weight  of  sample  used. 


APPENDIX  I.    LOGARITHMS  1OO  TO  1OOO 


381 


O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

10 

oooc 

0043 

008 

012 

017 

021 

025 

029 

033 

037 

481; 

I?  21    25 

29  33  38 

11 

12 
13 
14 
15 
16 
T7 
18 
19 
~2Q 

041 
079 
113 

^4b3 
0828 

H73 

049 
0864 
1206 

053 
089 
I23 

056 

093 
127 

060 
096 
130 

064 

100^ 

133 

068 
103 
136 

071 
107 
139 

075 
no 

143 

48i 
371 
361 

5  19  2 
4  17  2 
3  16  i 

26  30  •• 
24  28  31 
23  26  29 

140 

176 

204 

1492 
1790 
2068 

1523 
1818 
2095 

155 
184 
212 

i5«4 
187 
214 

ibi 
190; 
217 

1644 

193 

220 

167 
195 

222 

170 
198 

225 

173 

201 
227 

3  6 
36 
3  5 

2    5  * 
i     4  i 
1     3  i 

21    24   27 
20  22   25 

18  21  24 

2304 

255 
278 

2330 
2577 
2810 

2355 
2601 

2833 

238 
262 

285 

240 
2648 

2878 

2430 
267 
2900 

245 
269 
292 

2480 
271 

294 

2504 

274 
296 

252 
276 
298 

2  5 
2  5 

2  4 

10      2    I 

9    2  i 
9     i  i 

17   20   22 

16  19  21 

16  18  20 

3010 

3032 

3054 

307 

3096 

3ii 

313 

3160 

3i8 

320 

246 

8     i  i 

i5  17  19 

21 
22 
23 

3222 
3424 

3617 

3243 
3444 
3636 

3263 
3464 
3655 

3284 
3483 
3674 

3304 
3502 
3692 

3324 
3522 
37i 

334 
354 
372 

336 
3560 

3747 

338 
3579 
3766 

340 

359 

378 

246 
246 
246 

8    o  i 
8    o  i 
7    9  * 

14  16  18 
H  i5  17 
'3  '5  J7 
12  14  16 

12    14   15 
II    13    15 

24 
25 
26 
27 
28 
29 

3802 
3979 
4150 

3820 

3997 
4166 

3838 
4014 

4183 

3856 
403 
42OO 

3874 
4048 
4216 

3892 
4065 
4232 

390 
4082 
4249 

3927 
4099 
4265 

3945 
4116 
4281 

396 
413 
429 

2  4  -5 
235 
235 

7    9  * 
7    9  10 
7    8  10 

4314 
4472 
4624 

4330 
4487 
4639 

4346 
4502 
4654 

4362 

4518 
4669 

4378 
4533 
4683 

4393 
4548 
4698 

4409 
4564 
4713 

4425 
4579 
4728 

4440 
4594 
4742 

4456 
(.609 
4757 

235 
235 

i  3  4 

689 
680 
6    7    9 

II    I3    I4 
II    12    I< 
10   12    13 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

134 

6    7    9 

IO    II    I' 

31 

32 
33 

4914 
5051 

5185 

1928 
5065 
198 

4942 
5079 
5211 

4955 
5092 
5224 

4969 
5105 

5237 

4983 
5H9 
5250 

4997 
5132 
5263 

5011 

5145 
5276 

5024 

5159 
5289 

5038 
5172 
5302 

134 
i  3  4 
134 

6    7    8 
578 
5    6    8 

10   II    12 
9   11    12 

9  10  12 

34 
35 
36 

5315 
441 

563 

328 
453 
575 

5340 
5465 

5587 

5353 
5478 
5599 

5366 
5490 
5611 

5378 
5502 
5623 

5391 

5514 
5635 

5403 

5527 
5647 

54i6 

5539 
5658 

5428 

5551 
5670 

134 
124 

I    2     4 

S    6    8 
5    6    7 
5    6    7 

9  10  ii 
9  10  ii 
8  10  ii 

37 
38 
39 

682 
798 

QII 

694 
809 
922 

5705 

5821 

5933 

5717 

5832 
5944 

5729 
5843 
5955 

5740 

5855 
5966 

5752 
5866 
5977 

5763 

5877 
988 

5775 
5888 

5999 

5786 
5899 
6010 

123 
123 
123 

5    6    7 
5    6    7 
457 

8    9  10 
8    9  10 
8    9  10 

40 

021 

o3i 

6042 

6053 

6064 

6075 

6085 

096 

6107 

6117 

123 

456 

8    9  10 

41 

42 
43 

44 
45 

46| 

6128 
232 

335 

138 
243 

345 

6149 

6253 
6355 

6160 
6263 
6365 

6170 
6274 
6375 

6180 
6284 
6385 

6191 
6294 
6395 

2OI 
304 
405 

6212 
6314 
6415 

6222 
6325 
6425 

123 
2    3 

2   3 

456 

4    5    6 
4     5    6 

7    8    9 
7    8    9 
7    8    Q 

435 
532 
628 

444 
542 

637 

454 
55i 
646 

6464 
6561 
656 

474 
57i 
665 

6484 
6580 
6675 

6493 
590 

684 

503 

599 
693 

513 
609 
702 

522 
618 
712 

2  3 
2   3 

2    3 

4    5    6 
4    5    6 
4    5    6 

7    8    9 
7     8    9 
7    7    8 

47 
48 
49 

721 
812 
902 

730 

821 

QII 

6739 
6830 
6920 

749 
839 
928 

758 
848 

<m 

767 

857 
946 

776 
866 
Q^ 

785 
875 
q64 

794 
884 
Q72 

803 
893 
q8i 

2    3 

2   3 
2   3 

455 
445 
445 

6    7    8 
6    7    8 
6    7    8 

50 

qqo 

QQ8 

7007 

016 

024 

033 

042 

oso 

O^Q 

067 

2   3 

3     4     5 

6     7     b 

51 
52 

53 

076 
1  60 

243 

084 
168 

251 

7093 
7177 
7259 

101 

185 
267 

no 

193 

275 

118 

202 
284 

126 

210 
292 

135 
218 
300 

143 

226 
308 

152 
235 
316 

2    3 
2    2 
2     2 

345 
345 
345 

678 
6     7     7 
6    6    7 

54 

324 

332 

7340 

348 

356 

364 

372 

380 

388 

396 

2     2 

3     4     5 

6    6    7 

382 


APPENDIX  I.     LOGARITHMS   1OO  TO   1OOO 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

55 

56 
57 
58 

7404 

7412 

7419 

7427 

7435 

7443 

745i 

7459 

7466 

7474 

122 

345 

5  6  7 

7482 
7559 
7^34 

7490 
7566 
7642 

7497 
7574 
7649 

7505 
7582 
7657 

7513 
7589 
7664 

7520 

7597 
7672 

7528 
7604 
7679 

7536 
7612 
7686 

7543 
7619 
7694 

755i 
7627 
7701 

345 
345 

344 

5  6  7 
5  6  7 
5  6  7 

59 
60 
61 
62 

63 
64 

7709 
7782 
7853 

7716 

7789 
7860 

7723 
7796 

7868 

7803 
7875 

7738 
7810 
7882 

7745 
7818 
7889 

7752 
7825 
7896 

7760 
7832 
7903 

7767 

7839 
7910 

7774 
7846 
7917 

344 
344 
344 

5  6  7 

5  6  6 
5  6  6 

7924 
7993 
8o62 

793i 
8000 
8069 

7938 
8007 
8075 

7945 
8014 
8082 

7952 
8021 
8089 

7959 
8028 
8096 

7966 
8035 
8102 

7973 
8041 
8109 

7980 
8048 
8116 

7987 

8055 
8122 

334 

334 
334 

5  6  6 
SS^ 
5  5  £ 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

334 

5  5  t 

66 
67 
68 

70 

71 

8195 
8261 

8325 

8202 
8267 
8331 

8209 

8274 
8338 

8215 
8280 
8344 

8222 
8287 
8351 

8228 
8293 
8357 

8235 
8299 
8363 

8241 
8306 
8370 

8248 
8312 
8376 

8254 
8319 
8382 

334 
334 
334 

5  5  6 
5  5  6 
4-56 

8388 
8451 
8513 

8395 
3457 
8519 

8401 
8463 

8525 

8407 

8470 

8414 
8476 
8537 

8420 
8482 
8543 

8426 
8488 
8549 

8432 
8494 

8555 

8439 
8500 
8561 

8445 
8506 
8567 

234 
234 
234 

4  5  6 
4  5  6 
455 

72 
73 
74 
75 

8573 
8633 
8692 

8579 
8639 
8698 

8585 
8645 
8704 

8591 
8651 

8710 

8597 
8657 
8716 

8603 
8663 
8722 

8609 
8669 
8727 

8615 
8675 

8733 

8621 
8681 
8739 

8627 
8686 
8745 

234 
234 
234 

4  5 
4  5 
4  5 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

233 

4  5 

76 
77 
78 
79 
80 
81 

8808 
8865 
8921 

8814 
8871 
8927 

8820 
8876 
8932 

8825 
8882 
8938 

8831 
8887 
8943 

8837 
8893 
8949 

8842 
8899 
8954 

8848 
8904 
8960 

8854 
8910 
8965 

8859 
8915 
8971 

233 
233 
233 

4  5 
4  4 
4  4 

8976 
9031 
9085 

8982 
9036 
9090 

8987 
9042 
9096 

8993 
9047 
9101 

8998 

9053 
9106 

9004 
9058 
9112 

9009 
9063 
9117 

9015 
9069 
9122 

9020 
9074 
9128 

9025 
9079 
9*33 

233 
233 
233 

4  4 
4  4 
4  4 

84 

9^38 
9191 
9243 

9*43 
9196 
9248 

9149 
9201 
9253 

9154 
9206 
9258 

9r59 
9212 
9263 

9165 
9217 
9269 

9170 
9222 
9274 

9175 
9227 

9279 

9180 
9232 
9284 

9186 
9238 
9289 

233 
233 
233 

4  4 
4  4 
4  4 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335 

9340 

I 

233 

4  4 

86 
87 
88 

90 
91 

92 
93 
94 

9345 
9395 
9445 

9350 
9400 
9450 

9355 
9405 
9455 

936o 
9410 
9460 

9365 
9415 
9465 

9370 
9420 
9469 

9375 
9425 
9474 

938o 
9430 
9479 

9385 
9435 
9484 

9390 
9440 
9489 

I 
0 
0 

233 
223 
223 

445 
344 

3  4  4 

9494 
9542 
9590 

9499 
9547 
9595 

9504 
9552 
9600 

9509 
9557 
9605 

9513 
9562 
9609 

9518 
9566 
9614 

9523 
957i 
9619 

9528 
9576 
9624 

9533 
958i 
9628 

9538 
9586 
9633 

0 

o 

0 

223 
223 
223 

344 
344 
344 

9638 
9685 
973i 

9643 
9689 
9736 

9647 
9694 
9741 

9652 
9699 
9745 

9^57 
9703 
9750 

9661 
9708 
9754 

9666 
9713 
9759 

9671 
9717 
9763 

9^75 
9722 

9768 

9680 
9727 
9773 

o 
o 

0 

223 
223 
223 

344 
344 
344 

95 

96 
97 
98 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

o 

223 

344 

9823 
9868 
9912 

9827 
9872 
9917 

9832 
9877 
9921 

9836 
9881 
9926 

9841 
9886 
9930 

9845 
9890 

9934 

9850 
9894 
9939 

9854 
9899 
9943 

9859 
9903 
9948 

9863 
9908 
9952 

0 

o 

0 

223 
223 
223 

344 
344 
344 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

99C6 

Oil 

223 

334 

APPENDIX  II 


383 


SPECIFIC  GRAVITIES  OF  SULPHURIC  ACID 

Lunge  and  Isler 


Specific 
gravity 
15° 
4° 
in  vacuo 

100  parts 
by  weight 
correspond  to 
% 
H2SO4 

Specific 
gravity 
15° 
~4°~ 
in  vacuo 

100  parts 
by  weight 
correspond  to 

H2S04 

Specific 
gravity 
15° 
T5" 
in  vacuo 

100  parts 
by  weight 
correspond  to 
rt 

H2SO4 

1.000 

0.09 

1.205 

27.95 

1.410 

51.15 

1.005 

0.83 

1.210 

28.58 

1.415 

51.66 

1.010 

1.57 

1.215 

29.21 

1.420 

52.15 

1.015 

2.30 

1.220 

29.84 

1.425 

52.63 

1.020 

3.03 

1.225 

30.48 

1.430 

53.11 

1.025 

3.76 

1.230 

31.11 

1.435 

53.59 

1.030 

4.49 

1.235 

31.70 

1.440 

54.07 

1.035 

5.23 

1.240 

32.28 

1.445 

54.55 

1.040 

5.96 

1.245 

32.86 

1.450 

55  03 

1.045 

6.67 

1.250 

33.43 

1.455 

55.50 

1.050 

7.37 

1.255 

34.00 

1.460 

55.97 

1.055 

8.07 

1.260 

34.57 

1.465 

56.43 

1.060 

8.77 

1.265 

35.14 

1.470 

56.90 

1.065 

9.47 

1.270 

35.71 

1.475 

57.37 

1.070 

10.19 

1.275 

36.29 

1.480 

57.83 

1.075 

10.90 

1.280 

36.87 

1.485 

58.28 

1.080 

11.60 

1.285 

37.45 

1.490 

58.74 

1.085 

12.30 

1.290 

38.03 

1.495 

59.22 

1.090 

12.99 

1.295 

38.61 

1.500 

59.70 

1.095 

13.67 

1.300 

39.19 

1.505 

60.18 

1.100 

14.35 

1.305 

39.77 

1.510 

60.65 

1.105 

15.03 

1.310 

40.35 

1.515 

61.12 

1.110 

15.71 

1.315 

40.93 

1.520 

61.59 

1.115 

16.36 

1.320 

41.50 

1.525 

62.06 

1.120 

17.01 

1.325 

42.08 

1.530 

62.53 

1.125 

17.66 

1.330 

42.66 

1.535 

63.00 

1.130 

18.31 

1.335 

43.20 

1.540 

63.43 

1.135 
1.140 

18.96 
19.61 

1.340 
1.345 

43.74 
44.28 

1.545 
1.550 

63.85 
64.26 

1  145 

20.26 

1.350 

44.82 

.555 

64.67 

1.150 
1.155 
1.160 
1.165 
1.170 
1.175 
1.180 
1.185 
1.190 
1.195 
1.200 

20.91 
21.55 
22.19 
22.83 
23.47 
24.12 
24.76 
25.40 
26.04 
26.68 
27.32 

1.355 
1.360 
1.365 
1.370 
1.375 
1.380 
1.385 
1.390 
1.395 
1.400 
1.405 

45.35 

45.88 
46.41 
46.94 
47.47 
48.00 
48.53 
49.06 
49.59 
50.11 
50.63 

.560 
.565 
.570 
.575 
.580 
.585 
.590 
.595 
.600 
1.605 
1.610 

65.08 
65.49 
65.90 
66.30 
66.71 
67.13 
67.59 
68.05 
68.51 
68.97 
69.43 

384 


QUANTITATIVE  CHEMICAL  ANALYSIS 


SPECIFIC  GRAVITIES  OF  SULPHURIC  ACID    (Continued) 


Specific 
gravity 

15! 

4° 
in  vacuo 

100  parts 
by  weight 
correspond  to 

H2lo4 

Specific 
gravity 
15° 

"    .     4° 
in  vacuo 

100  parts 
by  weight 
correspond  to 
% 
H2S04 

Specific 
gravity 

15! 

4° 
in  vacuo 

100  parts 
by  weight 
correspond  to 
% 
H2SO4 

1.615 

69.89 

1.735 

80.24 

1.827 

91.50 

1.620 

70.32 

1.740 

80.68 

1.828 

91.70 

1.625 

70.74 

1.745 

81.12 

1.829 

91.90 

1.630 

71.16 

1.750 

81.56 

1.830 

92.10 

1.635 

71.57 

1.755 

82.00 

1.831 

92.30 

1.640 

71.99 

1.760 

82.44 

1.832 

92.52 

1.645 

72.40 

1.765 

82.88 

1.833 

92.75 

1.650 

72.82 

1.770 

83.32 

1.834 

93.05 

1.655 

73.23 

1.775 

83.90 

1.835 

93.43 

1.660 

73.64 

1.780 

84.50 

1.836 

93.80 

1.665 

74.07 

1.785 

85.10 

1.837 

94.20 

1.670 

74.51 

1.790 

85.70 

1.838 

94.60 

1.675 

74.97 

1.795 

86.30 

1.839 

95.00 

1.680 

75.42 

1.800 

86.90 

1.840 

95.60 

1.685 

75.86 

1.805 

87.60 

1.8405 

95.95 

1.690 

76.30 

1.810 

88.30 

1.8410 

97.00 

1.695 

76.73 

1.815 

89.05 

1.8415 

97.70 

1.700 

77.17 

1.820 

90.05 

1.8410 

98.20 

1.705 

77.60 

1.821 

90.20 

1.8405 

98.70 

1.710 

78.04 

1.822 

90.40 

1.8400 

99.20 

1.715 

78.48 

1.823 

90.60 

1.8395 

99.45 

1.720 

78.92 

1.824 

90.80 

1.8390 

99.70 

1.725 

79.36 

1.825 

91.00 

1.8385 

99.95 

1.730 

79.80 

1.826 

91.25 

APPENDIX  III  385 


LIST  OF  APPARATUS  NEEDED 

The  articles  which  are  named  in  the  following  list  represent  the  apparatus 
with  which  it  is  desirable  that  each  student  should  be  provided;  it  can  be 
modified  in  many  particulars  without  jeopardizing  the  success  of  his  work. 
For  many  of  the  determinations  which  are  described,  especially  those  out- 
lined in  Chapters  XII,  XIII,  XIV,  XV,  XXII,  XXVII,  XXX,  XXXI, 
XXXIII,  XXXIV,  XLIX  and  L,  additional  apparatus  is  necessary.  It 
will  be  found  desirable  to  prepare  a  series  of  boxes  containing  all  of  the  special 
articles  needed  for  each  of  these  determinations  and  give  them  out  to  the 
different  students  as  called  for. 

6-Beakers  of  Jena  glass  with  lips,  2-100  cc.,  2-250  cc.,  2-400  cc.,  1-600  cc., 
1-800  cc. 

2  Bottles  with  glass  stoppers,  2000  cc. 

2  Burets,  50  cc.     (1  Mohr  form  and  1  Geissler  form.) 

1  Bunsen  burner  with  rubber  tubing. 

1  Camel's  hair  brush. 

2  Clamps  to  hold  burets. 
-t-Desiccator  with  support  for  crucibles. 
^•Erlenmeyer  flasks,  2-100  cc.,  2-250  cc. 

1  Filter  flask  with  rubber  stopper,  500  cc. 
"2- -Filter  holders  (to  fit  cleats  on  desk). 

1  Package  washed  filters,  25-11  cm.,  20-9  cm.,  10-7  cm. 

1  Flask  of  Jena  glass,  1000  cc.,  with  2-hole  rubber  stopper  for  wash  bottle. 
-1  Flask  of  Jena  glass,    250  cc.,  with  2-hole  rubber  stopper  for  wash  bottle. 
1  Pair  forceps  of  nickel  or  brass. 
-4.Emmelsr2-5  cm.,  2-8  cm. 
•4-Gktss  filter  tube. 

4  Feet  glass  tubing,  6  mm.  in  diameter. 

3  Glass  rods,  20  cm.  long,  6  mm.  in  diameter. 

1  Piece  glazed  paper  30  cm.  square. 
Tt^rartaated  cylinder,  50  cc. 
•••Hron-stand  with  two  rings. 

2  Keys,  1  for  desk  and  1  for  drawer  to  balance. 
-3-Pipete,-  1-5  cc.,  1-10  cc.,  1-25  cc. 

1  Piece  platinum  wire  20  cm.  long  and  0.2  mm.  in  diameter. 

4  Porcelain  crucibles,  2-No.  000  (8  cm.),  2-No.  00  (12  cc.). 

1  Porcelain  Gooch  crucible  25  cc. 
-1  Porcelain  plate. 

2  Porcelain  casseroles  or  evaporating  dishes,  250  cc. 

1  Piece  fine  rubber  tubing,  20  cm.  long  and  6  mm.  in  diameter. 
4  Reagent  bottles,  for  dilute  acids  and  ammonium  hydroxide. 
%-Test  tubes,  1 5  cm. 
-£~Triaagles  of  nichrome  wire. 

1  Weighing  bottle,  30  cm. 

2  Piece&'0f-wie£ -gauze,      s 
4  Witt  filter  plate,  23  mm.  . 


INDEX 


Absorption  method  for  gas-evolution  processes,  82. 

Acetic  acid  in  vinegar,  determination  of,  299. 

Acids,  distillation  of,  71;   dissociation  constants  of,  288;   evaporation  of,  70; 

titration  with  an  acid  indicator,  281. 
Acid  salts,  titration  of,  287. 
Activity,  of  acids,  50;  of  bases,  51;  of  salts,  52. 
Adsorption,  129. 

Alkalies,  commercial,  analysis  of,  302. 
Alloys  of  lead  and  tin,  analysis  of,  180,  366. 
Alundum,  use  of,  119. 
Ames  extraction  apparatus,  200. 
Apparatus,  list  of,  for  quantitative  work,  385. 
Arsenious  acid  in  Paris  green,  determination  of,  345. 
Asbestos,  use  of,  for  filtration,  119. 
Atomic  weights,  table  of,  75. 

Baking  powder,  determination  of  carbon  dioxide  in,  103. 

Balance,  construction  of,  9;  rules  for  use  of,  22. 

Ball  mill  for  grinding,  28. 

Barium  sulfate,  ignition  of,  167;  properties  of,  166. 

Bases,  titration  of,  with  an  acidic  indicator,  288. 

Basic  salts,  titration  of,  289. 

Black  powder,  composition  of,  214;  analysis  of,  214. 

Boric  anhydride  in  borates,  determination  of,  301. 

Brass,  analysis  of,  185;  determination  of  copper  in,  346. 

Bumping,  cause  of,  68.        >, 

Bunsen  apparatus,  description  of,  99. 

Buoyancy,  correction  for,  20. 

Burets,  forms  of,  236. 

Caffeine  in  tea,  determination  of,  227. 
Calcium  carbonate,  decomposition  of,  78. 

387 


388  INDEX 

Calcium  chloride,  properties  of,  93. 

Calcium  oxalate,  properties  of,  173. 

Calcium  in  limestone,  determination  of,  324;  separation  of  from  magnesium, 
171;  theory  of  separation  of,  175. 

Calculations,  abbreviation  of,  76;  of  volumetric  determinations,  251. 

Calibration  of  burets,  244;  of  flasks,  245;  of  pipets,  245. 

Carbon  dioxide,  determination  of,  in  limestone,  99;  in  baking  powder,  103. 

Catalizers,  action  of,  47. 

Chaddock  burner,  65. 

Chalcopyrite,  determination  of  copper  in,  347. 

Chemical  factors,  calculation  of,  72. 

Chemical  formulae,  calculation  of,  77. 

Chlorine,  determination  of,  in  sodium  chloride,  150;  titration  of  with  silver 
solution,  253-254. 

Chromate  indicator,  use  of,  253. 

Chromium  in  chromite,  determination  of,  336. 

Cleaning  graduated  apparatus,  243. 

Cochineal,  use  of,  285. 

Colorimetric  processes,  principles  of,  370;  methods  of  making,  371;  limita- 
tions of,  374. 

Colorimeters,  371. 

Combustion  method,  theory  of,  84. 

Compensating  errors,  principle  of,  234. 

Complexions,  reactions  involving  formation  of,  59. 

Concentration,  definition  of,  31. 

Consolute  liquids,  216;  separation  of,  218. 

Continuous  extraction,  198. 

Copper,  determination  of,  in  slag,  378;  in  brass,  346;  in  chalcopyrite,  347. 

Copper,  separation  of,  by  electrolysis,  186;  by  aluminum,  347. 

Copper  sulfate,  dehydration  of,  81;  determination  of  water  in,  92. 

Counterpoise,  use  of,  in  weighing,  21. 

Crude  fat,  meaning  of,  210;  determination  of,  in  peanuts,  212. 

Crude  protein,  meaning  of,  303;  determination  of,  in  flour,  304. 

Cyanides,  reaction  of,  with  silver  salts,  256. 

Decantation,  127. 

Decomposition  voltage,  meaning  of,  138;  of  metals,  139. 

Dehydration  of  salts,  80. 

Dehydrating  agents,  efficiency  of,  92. 

Departure,  meaning  of,  90. 

Desiccator,  use  of,  29. 


INDEX  389 

Displacement  processes,  end  points  of,  276. 

Displacement  reactions,  58. 

Di-basic  acids,  titration  of,  286. 

Dissociation  pressures  of  carbonates,  79. 

Dissociation  of  electrolytes,  factors  affecting,  38. 

Dissociation  constants,  52;  of  acids,  50. 

Distribution  coefficient,  217. 

Double  precipitation,  139. 

Double  weighing,  12. 

Drainage,  error  from,  240. 

Drying,  devices  for,  62;  methods  of,  29. 

Electric  furnace,  68. 

Electro-neutrality,  law  of,  48. 

Electrodes,  efficiencies  of  different,  142;  forms  of,  140-142. 

Electrode  potential,  determination  of,  310;  table  of,  311. 

Electrolytic  dissociation  theory,  development  of,  35;  importance  of,  40. 

Electrolytic  precipitation,  effect  of  current  strength  on,  142;  effect  of  con- 
centration on,  144. 

End  point,  meaning  of,  232;  recognition  of,  in  processes  involving  neutral- 
ization, 278;  oxidation,  313;  in  titrations  with  silver,  252. 

Equilibrium,  41;  effect  of  temperature  on,  44;  of  pressure  on,  44. 

Equilibrium  constant,  43. 

Ether,  purification  of,  211. 

Evaporation,  devices  for,  61. 

Evolution  method,  82. 

Extraction  processes,  197. 

Factor  weights,  use  of,  79. 

Faraday,  law  of,  142. 

Fat,  chemical  nature  of,  210;  determination  of,  212. 

Filtering  tube,  use  of,  121. 

Filtration,  devices  for,  119;  media  used  for,  118. 

Gangue  matter,  meaning  of,  171. 

Gooch  crucible,  122. 

Gypsum,  determination  of  water  in,  89;  properties  of,  87. 

Hematite,  determination  of  iron  in,  334. 
Heterogeneous  equilibrium,  41. 
Homogeneous  equilibrium,  41. 


390  INDEX 

Hydriodic  acid,  substances  reduced  by,  343. 
Hydrocyanic  acid,  indirect  determination  of,  291. 
Hydrolysis,  reactions  involving,  57. 
Hydrometers,  calibration  of,  362. 
Hygroscopic  water,  20. 

Ignition  of  precipitates,  127. 

Index  of  refraction,  uses  of,  354. 

Indicator  constant,  280. 

Indicator  theory,  first  case,  232;  second  case,  233. 

Indirect  determinations,  290. 

Intermittent  extraction,  199. 

Interpolation  methods,  use  of,  353. 

Iodine,  as  an  oxidating  agent,  339;  substances  oxidized  by,  342. 

Iodine  solution,  preparation  of,  340;  standardization  of,  341. 

lodometric  processes,  340. 

Ions,  36;  formation  of  complex,  57,  59. 

Iron,  determination  of,  in  cast  iron,  320;   in  ferrous  ammonium  sulfate,  159; 

in  ores,  334;  errors  in  determination  of,  172. 
Iron,  methods  of  reducing,  320;  separation  of  by  ammonium  hydroxide,  165; 

separation  from  nickel,  221. 
Iron  ores,  decomposition  of,  332. 
Isohydric  solutions,  54. 

Jones  reductor,  321;  use  of,  322. 

Kainite,  determination  of  chlorine  in,  259. 
Kjeldahl  method,  304. 
Knorr  extraction  apparatus, 

Lead  sulfate,  properties  of,  181. 

Lead  tin  alloy,  analysis  of,  180,  366. 

Limestone,  analysis  of,  171;  determination  of  carbon  dioxideln,  99. 

Lindo-Gladding  method  for  potassium,  206. 

Logarithms,  table  of,  381. 

Magnesium  ammonium  phosphate,  precipitation  of,  155;  ignition  of,  156. 

Magnesium  in  magnesium  sulfate,  determination  of,  156. 

Magnesium  oxalate,  properties  of,  174. 

Manganese,  determination  of,  in  cast  iron,  377 ;  colorimetric  method  for,  375. 

Mass  action,  law  of,  42. 

Measurement  of  volumetric  solutions,  236. 


INDEX  391 

Meker  burner,  64. 

Metastannic  acid,  properties  of,  180. 

Mercury,  determination  of,  107. 

Methyl  orange,  use  of,  284. 

Mixing  of  samples,  27. 

Mixtures  with  additive  properties,  351. 

Modulus  of  hydrometers,  362. 

Moisture,  determination  of,  28. 

Monobasic  acids,  titration  of,  286. 

Muffle,  use  of,  62;  for  heating  tubes,  53. 

Multiple  extraction  apparatus,  202. 

Nessler's  cylinders,  373. 

Neutralization,  reactions  involving,  273. 

Nickel,  determination  of,  in  nickel  steel,  223. 

Normal  system  for  standard  solutions,  248;  advantages  of,  250. 

Occlusion,  factors  affecting,  130,  133;   methods  of  avoiding  errors  frorr,  135; 

theories  of,  129. 
Oxidation  and  reduction,  306. 
Oxidation  and  theory  of  the  galvanic  cell,  309. 
Oxidizing  agents,  normal  values  of,  308. 
Oxidizing  capacity,  306. 
Oxidizing  potential,  309. 

Paralax,  errors  from,  238. 

Para-nitro-phenol,  use  of,  285. 

Paris  green,  determination  of  arsenic  in,  345. 

Partition  processes,  theory  of,  219. 

Peanuts,  composition  of,  211;  determination  of  fat  in,  212. 

Petroleum,  determination  of  specific  gravity  of,  368. 

Percentage  error,  90. 

Permanganates,  formation  of,  375. 

Phase,  definition  of,  3. 

Phenolphthalein,  color  changes  of,  279;  uses  of,  285, 

Phosphoric  acid,  indirect  determination  of,  291. 

Physical  constants,  uses  of,  350. 

Pipets,  forms  of,  237;  errors  in  using,  240. 

Point  of  rest  of  balance,  14;  method  of  determining,  23. 

Potassium  in  potassium  sulfate,  determination  of,  205. 

Potassium  bitartrate,  determination  of,  300. 


392  INDEX 

Potassium  cyanide,  determination  of,  260. 

Potassium  chloroplatinate,  formation  of,  205;  properties  of,  206. 

Potassium  dichromate,  end  points  with,  330;  factors  affecting  reaction  with, 

329;  oxidizing  capacity  of,  328;  oxidizing  potential  of,  328;  preparation 

of  standard  solutions  of,  331. 
Potassium  ferrocyanide,  factors  affecting  reaction  with  zinc,  265;  preparation 

of  a  standard  solution  of,  268. 
Potassium  nitrite,  determination  of,  324. 
Potassium   permanganate,   factors   affecting  reactions   with,    315;  oxidizing 

potential,  314;  oxidizing  capacity,  314;  standardization  of,  318;  uses  of, 

316. 

Precipitation  processes,  general  theory  of,  111. 
Precipitates,  classes  of,  122;  solubility  of,  111. 
Pycnometer,  use  of,  359. 

Quantitative  processes,  classes  of,  2. 

Reaction  constant,  43. 

Reading  burets,  244. 

Reduction  of  iron,  methods  of,  320;  by  stannous  chloride,  333. 

Repression  of  ionization,  55. 

Reversible  reactions,  45. 

Rosolic  acid,  use  of,  285. 

Sampling,  theory  of,  26. 

Selection,  methods  of,  27. 

Sensitiveness  of  balance,  13;  of  indicators,  283. 

Separatory  funnel,  use  of,  218. 

Separation  of  closely  related  ions,  115. 

Silicates,  decomposition  of,  190. 

Silica  in  hornblende,  determination  of,  190. 

Silicic  acid,  dehydration  of,  191. 

Silver  chloride,  properties  of,  150;  theory  of  precipitation  of,  113. 

Silver  nitrate,  preparation  of  standard  solution  of,  257. 

Slags,  decomposition  of,  379. 

Soda  lime,  properties  of,  103. 

Sodium  oxalate,  uses  of,  319. 

Solder,  analysis  of,  180. 

Solid  mixtures,  analysis  of,  365. 

Solubility,  31;  effect  of  size  of  particles  on,  33;  of  gases,  31. 

Solubility  product,  31. 


INDEX  393 

Solutions,  30. 

Solution  processes,  theory  of,  195. 

Solvent,  30. 

Soxhlet  tube,  199. 

Specific  gravity,  357;  determination  of,  358-359. 

Specific  rotary  power,  355.£ 

Specific  volume,  351. 

Splitting  a  watch  glass,  160. 

Stammar's  colorimeter,  372. 

Standard  solution,  230. 

Stirring  devices  in  electrolytic  precipitations,  149. 

Strength  of  acids  and  bases,  39. 

Sulfides,  methods  of  oxidizing,  164. 

Sulfur  in  pyrites,  determination  of,  164. 

Sulfuric  acid,  determination  of,  299;  specific  gravity  of,  383. 

Superheating,  67. 

Supersaturation,  32. 

Tap  water,  determination  of  chlorine  in,  259. 

Tea  leaves,  composition  of,  226;  determination  of  caffeine  in,  227. 

Temperature  changes  in  measuring  solutions,  241,  243. 

Temperature  attainable  with  burners,  63. 

Thiosulfate  solution,  preparation  of,  345. 

Titration,  230. 

Unit  of  volume,  242. 

Unitary  system  for  standard  solutions,  247. 

Valence,  positive  and  negative,  306. 
Van't  Hoff,  law  of,  34. 
Vapor  pressures  of  mixed  liquids,  69. 

Volumetric  processes,  advantages  of,  234;  reactions  suitable  for,  231;  theory 
of,  230. 

Wash  bottle,  preparation  of,  151. 

Washing  precipitates,  theory  of,  125. 

Water,  determination  of,  in  copper  sulfate,  96;    in  gypsum,  89;    reactions 

involving  formation  of,  56. 

Weighing,  abbreviated  method  of,  17;  accurate  method  of,  16. 
Weights,  calibration  of,  19,  25. 
Westphal  balance,  364. 


394  INDEX 

Whitton's  apparatus,  108. 

Wiley  extraction  apparatus,  199. 

Wiring  of  bench  for  electrolytic  determinations,  146. 

Witt  filter  plates,  121. 

Wolff's  colorimeter,  372. 

Zinc,  determination  of,  as  phosphate,  186;  determination  of,  in  an  ore,  269, 
271;  effect  of  temperature  on  titration  of,  265;  effect  of  acid  on  titration 
of,  267;  effect  of  concentration  on  titration  of,  266. 


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